What *is* intrinsically real? Is the "unconditioned", "absolute", or "ultimate" intrinsically real?

It has been said that all phenomena are conditioned, not intrinsically real

When you asked that, you were quoting an answer of Yeshe Tenley's.

I think the Pali doesn't say "all phenomena are conditioned", but it does talk about "conditioned phenomena" (sankhara) ... and refers to Nibbana as "the Unconditioned" (and other epiphets) ... see also What are conditioned as opposed to unconditioned phenomena?

I think that the doctrine which Yeshe Tenley was explaining says that Nibbana too is "not intrinsically real". There's an example of that in this answer and its comments; and maybe this comment is a reference to detailed explanations:

You said, "I don't know how to reconcile that with the doctrine that "nibanna isn't conditioned" (or "is unconditioned")." I'd suggest that a careful study of Chapter 25 of Nagarjuna's Fundamental Treatise of the Middle Way along with the excellent commentary by Je Tsongkhapa in Ocean of Reasoning might help to understand this.

So what is intrinsically real?

I don't know how other people understand the term "intrinsically real".

I think (in classic English) that the word "real" meant "thing-like": maybe substantial or tangible. An opposite of "real" might be "ideal", i.e. an idea as opposed to a thing. According to that classification, the body might be "real" but a feeling might not be (a feeling is more "ideal", i.e. idea-like rather than thing-like). I wouldn't necessarily mean that a feeling is imaginary or non-existent, but it's not substantial nor exactly tangible.

Related to that is the idea of reifying ideas, i.e. the process of treating ideas as if they were real. As you can see from that Wikipedia link (which isn't even Buddhism-specific) that's a complex topic or a set of related topics: different topics include "linguistics" (talking about ideas as if they're real), psychology (perceiving ideas as if they're real), and as a type of fallacy (a type of logical mistake, e.g. mistaking an idea for reality when it's really only an idea, and maybe not even a 'true' one).

I say this to illustrate that the English language or meaning (of the word "real") is complicated, and if you assume you know what it means that might be misleading.

I might add that that emphasis on what's "real", in the sense I described it, might be missing the whole point, from a Buddhist point of view: because Buddhists might dismiss that as mere "materialism".

I'm not sure what "intrinsically" means, either. I think it's used to argue that all composite things, at least, aren't intrinsically real in the sense that, for example, "a chair isn't intrinsically a chair: because if you disassemble it, take it apart, then it isn't a chair anymore".

And I'm not sure what "relative" means. I assume it means that a property exists as a result of comparing one thing relative to another: for example a mountain is high because a valley is low, or shadow is cold because sunshine is warm, and so on -- which I think is central to the Taoist doctrine of Yin and Yang. I'm not sure (I doubt) whether that (relativism) is so prevalent in the Pali. The Pali is very dualistic, IMO, e.g. it consists of doctrine about whether an action is "skilful" versus "not skilful" ... I'm pretty sure it wouldn't say that these aren't real just because they're relative. Another meaning of "relative" I guess might be that it's an artefact of a relationship with the observer: e.g. what I perceive as a "tree" isn't real, that's just an artefact of contact between the tree-as-sense-object with the sense-organs (e.g. the eye), and memories and linguistic associations ("that collection of sense-impressions may be called 'a tree'"), and changes (or vanishes) e.g. when the observer moves.

There's a Pali sutta called the Tatha Sutta ("Real": SN 56.20):

Tatha Sutta: Real

Monks, these four things are real, not unreal, not otherwise. Which four?

"'This is stress,' is real, not unreal, not otherwise. 'This is the origination of stress,' is real, not unreal, not otherwise. 'This is the cessation of stress,' is real, not unreal, not otherwise. 'This is the path of practice leading to the cessation of stress,' is real, not unreal, not otherwise.

"These are the four things that are real, not unreal, not otherwise.

"Therefore your duty is the contemplation, 'This is stress... This is the origination of stress... This is the cessation of stress... This is the path of practice leading to the cessation of stress.'"

The Pali word that's translated as "real" is tatha. Tatha is used in the word tathagatta and also (as well as "real") means "true" ... or "so" (in the phrase, "that is so") or "such".

Anyway that illustrates another meaning of "real": i.e. it means "true". Even in (non-Buddhist) English, something (especially a story) that's "fabricated" implies it might be untrue, or at least (if it's a consumer product) unreliable, disposable, transient.

The Buddha did teach emptiness in the Pali Suttas, but it is restricted to the nature of the self i.e. all phenomena is empty of a self (see Shunya Sutta). The Buddha did not comment on the nature of all non-sentient things like the universe, besides noting them as being conditioned, compounded and impermanent.

The Buddha was not interested in commenting on the nature or origin of the universe, because he considered it to be unimportant to the path to liberation from suffering - see the Parable of the Poisoned Arrow (from MN63). The Buddha was not interested in metaphysical speculations (also see Simsapa Sutta). This is also the stand of Theravada Buddhism today.

While the Buddha (of the Pali Suttas) stopped at describing the "middle way" (between eternalism and annihilationism) and emptiness with respect to the nature of the self, Mahayana philosopher Nagarjuna expanded these concepts to cover the nature of the universe and all reality.

Rather than the annihilationism that nothing exists or the eternalism that something exists eternally, Nagarjuna taught the "middle way" that all phenomena is empty of its own "inherent existence" or "substance" or "essence" (what he called svabhāva).

If nothing has inherent substance, then nothing can depend on something else for substance, so there is no other inherent substance (para-bhāva).

A key concept of Madhyamaka is that even this emptiness is empty i.e. this emptiness does not have its own inherent substance. This means that there is no transcendental reality beyond phenomenal reality. This is what is implied by ultimate reality not being absolute reality.

A very nice and simplified explanation of the Madhyamaka emptiness can be found in Zen master Thich Nhat Hanh's writing, "The Fullness of Emptiness". I quote some parts of it below:

If you are a poet, you will see clearly that there is a cloud floating in this sheet of paper. Without a cloud, there will be no rain; without rain, the trees cannot grow; and without trees, we cannot make paper. The cloud is essential for the paper to exist. If the cloud is not here, the sheet of paper cannot be here either. We can say that the cloud and the paper inter-are. “Interbeing” is a word that is not in the dictionary yet, but if we combine the prefix “inter-” with the verb “to be,” we have a new verb, “inter-be.”

If we look into this sheet of paper even more deeply, we can see the sunshine in it. If the sunshine is not there, the forest cannot grow. In fact, nothing can grow. Even we cannot grow without sunshine. So we know that the sunshine is also in this sheet of paper. The paper and the sunshine inter-are. And if we continue to look, we can see the logger who cut the tree and brought it to the mill to be transformed into paper. And we see the wheat. We know that the logger cannot exist without his daily bread, and therefore the wheat that became his bread is also in this sheet of paper. And the logger’s father and mother are in it too. When we look in this way, we see that without all of these things, this sheet of paper cannot exist. .....

When Avalokita says that our sheet of paper is empty, he means it is empty of a separate, independent existence. It cannot just be by itself. It has to inter-be with the sunshine, the cloud, the forest, the logger, the mind, and everything else. It is empty of a separate self. But, empty of a separate self means full of everything. So it seems that our observation and that of Avalokita do not contradict each other after all. Avalokita looked deeply into the five skandhas of form, feelings, perceptions, mental formations, and consciousness, and he discovered that none of them can be by itself alone. Each can only inter-be with all the others. So he tells us that form is empty. Form is empty of a separate self, but it is full of everything in the cosmos. The same is true with feelings, perceptions, mental formations, and consciousness.

Form is the wave and emptiness is the water. To understand this, we have to think differently than many of us who were raised in the West were trained to think. In the West, when we draw a circle, we consider it to be zero, nothingness. But in India and many other Asian countries, a circle means totality, wholeness. The meaning is the opposite. So “form is emptiness, and emptiness is form” is like wave is water, water is wave. “Form is not other than emptiness, emptiness is not other than form. The same is true with feelings, perceptions, mental formations, and consciousness,” because these contain each other. Because one exists, everything exists.

So, to answer your question, something that's intrinsically real, is something that has separate, independent existence. Since the sheet of paper does not have separate, independent existence, so it's not intrinsically real. According to this concept, you cannot find a true boundary where the paper ends and the rest of the universe begins. They all depend on each other.

It really depends upon the level of the disciple. The Buddha taught different stages of understanding of reality and each progressively works on adding subtlety to the understanding of reality.

In the First Turning of the Wheel of Dhrama, the Buddha taught about the five aggregates and how they are impermanent and the self itself is impermanent. He went on to explore the self and how it cannot be found as one with the aggregates or separate from the aggregates thus expounding the concept of selflessness. Then in the Second Turning of the Wheel of Dharma, the Buddha taught the perfection of wisdom where he refuted the existence of even the five aggregates. However since these were two rather extreme views, the Buddha taught in the Third Turning of the Wheel of Dharma about the view that things exist in the mind-only.

The above is a rather simplistic essence, but what the Buddha was doing during the three turnings was introducing the nature of reality from the less subtle to the most subtle understanding.

We have to realize, that we may not be ready for the most subtle understanding of reality just yet and have to work our ways up the levels of subtlety.

Sometimes it does help to look at metta as truly existing. At times it helps to look at a basal consciousness and karmic imprints as existing. It can also help by looking at conventional and ultimate reality as two modes. Or you may be better of looking at the Madhayamika Prasangika view of the absence of inherent existence and the reality that is solely based on dependant origination.

So to answer your question if metta is real, the best way to look at it would be from understanding your own understanding and how it corresponds to the four schools of tenets and working the way up.

https://studybuddhism.com/en/advanced-studies/abhidharma-tenet-systems/the-indian-tenet-systems/the-four-buddhist-tenet-systems-regarding-the-self

All phenomena(Dhamma) are real. Metta is real. Anger is real. There's nothing relative about it.

All phenomena are grouped into 4 categories

1. Rupa - form
2. Citta - consciousness
3. Cetasika - concomitants of consciousness
4. Nibbana

Metta(kindness), anger(Dosa), ignorance(Moha) etc. come under Cetasika. They are all real.

Emptiness in Buddhism does not mean "not real". It just means empty of satisfaction, empty of permanence, empty of a self. Here's a related video.

Nothing whatsoever is intrinsically real. Metta is not intrinsically real. The Tathagata is not intrinsically real. Nirvana is not intrinsically real. Emptiness is not intrinsically real. To be very clear, I'm not saying "nothing" taken as subject is intrinsically real either. If you could point to even one intrinsically real thing, then all this ^^^^^ would be refuted.

The word "intrinsically" in the phrase "intrinsically real" signifies that it is being used synonymously or mutually inclusively with inherent existence. This is not always the case.

Sometimes the word "real" is not used synonymously with inherent existence, but rather it is used to signify things that appear in concordance with how they actually exist. Under this definition, there is only one real thing: emptiness or the lack of inherent existence. That is to say, the only real thing - in that it appears the way it actually exists - is emptiness. All other things are false in the sense that they appear discordant with how they actually exist. They appear to us as having inherent existence, but they actually do not have inherent existence even in the slightest; thus they are unreal or false.

To ordinary beings who don't understand the unreality of things, phenomena like a face in a mirror [or a mirage of water, dreams, a snake imputed on a rope etc.,] are considered unreal in contradistinction to so-called real things. It is easy for ordinary beings to see that a face in the mirror is unreal ie., that it does not exist in concordance with how it appears. However, it is very hard for us to see that other phenomena that we regard as "real" ... are actually completely unreal.

The Prasangika Madhyamaka tenet system as elucidated by Je Tsongkhapa is considered by some the definitive and most subtle understanding of the doctrine emptiness. Under this system:

1. Only in relation to the world - ie., ignorance - it is said that some phenomena are real and some are unreal.
2. However, all things - save emptiness - are actually unreal ie., they do not exist in concordance with how they appear.
3. All things lack inherent existence including emptiness itself.

So how do the Four Noble Truths actually exist for instance? They exist utterly empty of inherent existence. They exist in dependence on conditions. It is easy to see how the First Noble Truth is dependent. The Buddha has taught that suffering is not permanent. If suffering is not dependently arisen, then it could not be impermanent.

What about "The Four Noble Truths" as an abstract concept? I hope it goes without saying that abstract concepts are not intrinsically real. One might say they exist, but of course they are dependent upon conditions including the mind that conceives them or communicates them.

Generally speaking, there are different forms of dependence. Dependence on causes and conditions, dependence on parts, dependence on name and form, dependence on a basis of designation and labels, etc. All existing and non-existing things (like the son of a barren woman) are included in the selfless. Even permanent things like uncompounded space are included in the selfless.

Objection! If they do not exist inherently, then they must not exist at all like the son of a barren woman!

Nagarjuna gives voice to this objection and then refutes it in the Fundamental Treatise on the Middle Way:

If all this is empty,
There would be neither arising nor ceasing,
And for you, it follows that
The Four Noble Truths do not exist.

Nagarjuna then goes on to give 5 more verses of objections in Chapter 24 before he responds with:

Here we say that you do not understand
Emptiness, or the purpose of emptiness,
Or the meaning of emptiness.
As a consequence you are harmed by it.

The Buddha’s teaching of the Dharma
Is based on two truths:
A truth of worldly convention,
And an ultimate truth.

Je Tsongkhapa in his Ocean of Reasoning commentary on Nagarjuna's Fundamental Treatise gives extensive explanation of the refutation. I will invite you to read it along with Nagarjuna's Treatise and here only repeat Nagarjuna:

If all this were nonempty, as in your view,
Then there would be no arising and ceasing.
It would follow that the
Four Noble Truths Would not exist.

Warning:

If you take anything I've said above as indicating that nothing exists or that this line of thought refutes the Four Noble Truths, Karma, Rebirth, the Dharma, the Buddha, the Path and the Fruits, etc., then I've miscommunicated and I apologize. Nothing could be further than the truth! Consider this warning a handrail to lean on if you take the above to indicate nihilism:

By a misperception of emptiness
A person of little intelligence is destroyed:
Like a snake incorrectly seized,
Or like a spell incorrectly cast.

You can't walk under a rainbow - in this sense it is an illusion. And yet rainbow is a meteorological phenomenon that actually occurs - in this sense it is not an illusion.

In Mahayana Buddhism we say that the rainbow is "empty". Meaning, if we disassemble it, there is nothing inside, no core, no secret ingredient. If we examine it closely, we will see the water droplets, the sunlight, the reflection, refraction, dispersion, and the observer looking at it from a certain angle - all these things combined lead to appearance of an arch in the sky - but in actuality there is no arch.

When you see a homeless person, and out of pity give him money for food - on one hand that's real metta-karuna operating in you. On the other hand, giving him money won't really change anything. Perhaps it actually makes it worse, by enabling him to buy alcohol. Perhaps if you took him home by force and taught Dharma - that would be actual help, but you don't do that. So maybe it's not metta, maybe it's ignorance operating in you. Or perhaps, who knows - may be the homeless person should feel pity for you, because he can wander unfettered and you have to go to work every day. In that sense, maybe it's not metta, maybe it's conceit operating in you. In that sense, our metta is not real. Who can judge whether our kindness is real kindness or fake kindness? It depends on the judge. And yet we try to be as kind as we can, and as wise as we can. So metta is like rainbow - depends on the object, the situation, and the position of the observer.

According to Mahayana (specifically the part called Madhyamaka - "the meaning of the middle way"), everything is like that: on one hand it's real - and on the other hand it's not; on one hand it exists - and on the other hand it's an illusion; it looks solid from afar - but falls apart under careful examination. Nothing is real - and yet everything is real.

They say even this ^^^ understanding above is not "real", because it is only a conceptual map - and map is never exactly the same as the territory.

In this sense nothing is intrinsically real. All our experiences are like "rainbows" in some sense. All our concepts are like "maps". Even Nirvana is just a word that gives a label but does not really explain anything. Entire Dharma is a map or a guidebook that only approximately explains what happens in real life.

In Mahayana we say that going beyond these rainbows and maps (="Realizing Emptiness"), is a big step towards Enlightenment.

Now, depending on a particular school we either say that the actual "ground reality" beyond the rainbows and maps (=ontological reality behind experiences and descriptions) is intrinsically real. OR we say that there is no such absolute ground and everything is completely relative. If you belong to Nyingma or Kagyu - then you say that the ground reality is real, just indescribable and not accessible to direct experience, but we actually are living it. And if you belong to Gelug, then you say that this ground is only an abstraction in our mind, leaving us with nothing to stand on. This is known as the Rangtong-Shentong distinction.