How to reconcile the "right view" in the Noble Eightfold path with Snp 4.5?

Both statements can be valid, if you consider that the statement regarding realization is non-dualistic. Otherwise said:

AN 3.136 is an upaya, a dualistic description of reality to direct the practitioner in the right "direction".

SNP 4.5 is the perspective of a "realized one", meaning that he/she no longer sees a separation between him/her and the world.

Otherwise said: all things are empty of intrinsic existence and nature, and since a "view" requires an observer and something to be observed, the concept of "view" in itself is dualistic and therefore cannot be a non-dualistic expression. This is expressed in SN 4.5 as taking a view not making oneself free of "dispute", since taking a view inherently creates a separation between "my" view and "other" views (e.g. duality).

As Bonn has explained, "holding a view" means clinging to a view (ditthi-upadana). The fully enlightened ones no longer have clinging (upadana).

The fully enlightened ones see things as they truly are (yathabhutam pajanati).

The fully enlightened ones see the universal laws (the three marks of existence from AN 3.136) as they are, without having to cling to them as a view. They do not have papanca, meaning they do not objectify and classify what is sensed and perceived, relative to the self.

“Bhikkhus, the Tathāgata, too, accomplished and fully enlightened, directly knows earth as earth. Having directly known earth as earth, he does not conceive himself as earth, he does not conceive himself in earth, he does not conceive himself apart from earth, he does not conceive earth to be ‘mine,’ he does not delight in earth. Why is that? Because the Tathāgata has fully understood it to the end, I say.

“He too directly knows water as water… Nibbāna as Nibbāna… Why is that? Because the Tathāgata has fully understood it to the end, I say.
MN 1

“Mendicants, whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles: all conditions are impermanent. A Realized One understands this and comprehends it, then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it: ‘All conditions are impermanent.’

Whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles: all conditions are suffering. A Realized One understands this and comprehends it, then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it: ‘All conditions are suffering.’

Whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles: all things are not-self. A Realized One understands this and comprehends it, then he explains, teaches, asserts, establishes, clarifies, analyzes, and reveals it: ‘All things are not-self.’”
AN 3.136

I read with interest the answers by Linda Blanchard and ChrisW, in which they suggest that the "view" of Snp 4.5 is about mere opinions, or conceited opinions, and this is not the same as the noble Right View, unless correct knowledge and understanding of the Dhamma is used for conceited disputes, as shown in the snake simile of MN 22.

I disagree with this, because the same statement appears elsewhere too, like Snp 1.8:

By not holding to fixed views,
The pure-hearted one, having clarity of vision,
Being freed from all sense desires,
Is not born again into this world.
Snp 1.8

I feel that the noble Right View of MN 117 is good and correct, and is a factor of the path for noble disciples who are still striving for Nibbana.

However, the fully enlightened ones (arahants and Buddhas) have let go of all views as in they have stopped clinging to views, even the noble Right View.

This is explained by the Buddha using the raft simile of MN 22.

“Bhikkhus, suppose a man in the course of a journey saw a great expanse of water, whose near shore was dangerous and fearful and whose further shore was safe and free from fear, but there was no ferryboat or bridge for going to the far shore. Then he thought: ‘There is this great expanse of water, whose near shore is dangerous and fearful and whose further shore is safe and free from fear, but there is no ferryboat or bridge for going to the far shore. Suppose I collect grass, twigs, branches, and leaves and bind them together into a raft, and supported by the raft and making an effort with my hands and feet, I got safely across to the far shore.’ And then the man collected grass, twigs, branches, and leaves and bound them together into a raft, and supported by the raft and making an effort with his hands and feet, he got safely across to the far shore. Then, when he had got across and had arrived at the far shore, he might think thus: ‘This raft has been very helpful to me, since supported by it and making an effort with my hands and feet, I got safely across to the far shore. Suppose I were to hoist it on my head or load it on my shoulder, and then go wherever I want.’ Now, bhikkhus, what do you think? By doing so, would that man be doing what should be done with that raft?”

“No, venerable sir.”

“By doing what would that man be doing what should be done with that raft? Here, bhikkhus, when that man got across and had arrived at the far shore, he might think thus: ‘This raft has been very helpful to me, since supported by it and making an effort with my hands and feet, I got safely across to the far shore. Suppose I were to haul it onto the dry land or set it adrift in the water, and then go wherever I want.’ Now, bhikkhus, it is by so doing that that man would be doing what should be done with that raft. So I have shown you how the Dhamma is similar to a raft, being for the purpose of crossing over, not for the purpose of grasping.

“Bhikkhus, when you know the Dhamma to be similar to a raft, you should abandon even the teachings, how much more so things contrary to the teachings.
MN 22

After writing this, I noticed that Arkaprava Paul quoted the same sutta.

Is the “right view” as described in the Noble Eightfold Path the same kind of “view” that is described in Snp 4.5?

Snp 4.5 is describing conceit, associated with disputes.

Wikipedia

Māna (Sanskrit, Pali; Tibetan: nga rgyal) is a Buddhist term that may be translated as "pride", "arrogance", or "conceit". It is defined as an inflated mind that makes whatever is suitable, such as wealth or learning, to be the foundation of pride.1 It creates the basis for disrespecting others and for the occurrence of suffering.

See also How are 'conceit' and 'identity-view' not the same?

I guess it -- disputes about the Dhamma -- was a common problem among monks or other wanderers, see also the famous Ud 6.4.

If so, does this mean that a Realized One abandons a profound universal truth which is true whether a Realized One arises or not?

Part of the message I get from MN 22 is to avoid reading too much into, avoid inferring too much from, the buddha-vanaca -- it says what it says, and that's what it says. Note the Translator's Introduction:

Regardless of how Arittha actually arrived at his position, the Commentary's suggestion makes an important point: that just because an idea can be logically inferred from the Dhamma does not mean that the idea is valid or useful.

So the point is to understand what the Noble Truths are -- not to pose a dilemma, question whether they should or shouldn't be held -- apparently the point is to grasp them (as in the Water-snake simile), and not to use them "both for attacking others and for defending themselves in debate" (back to the topic of disputes).

I find Piya Tan's a fairly detailed analysis, 50-odd pages, of what the Four Noble Truths are or what the Buddha says about them. Here is an excerpt:

There is something there about what "Realised" means, i.e. the objects become "perfect" or past-tense: "has been"...

You seem familiar with the doctrine that the Buddha is trackless, so... and I guess that "abandoning" truth might be one extreme, and that that extreme might have some opposite extreme, and neither extreme description is applicable to the Unbound.

Another sutta (in terms of what the suttas actually say), SN 6.2 describes what the Buddha says is his attitude towards the Dhamma.

Enlightenment is important for reading Sutta, or at least memorizing. Actually, the noble one in love with memorizing Sutta, so it's same ^.^

It’s been asserted that the Four Noble Truths were profound universal truths as described in AN 3.136. The Four Noble Truths include the Noble Eightfold Path which importantly includes “right view” as the first step on that path.

In DN22 SammaDitthi of SaccaPabba, right view is professional understanding of the four noble truth.

The right view is a factor of knower, 4 noble truth is the object.

However, it is said in Snp 4.5 that a Realized One does not hold any “views” nor declare any view foremost:

“Whoever should take to himself certain views, thinking them best, supreme in the world, and hence he proclaims all others as low— by this he does not become free from disputes.“

Holding means clinging, craving, addict.

Holding on View means DitthUpadana.

Upadana must arising with Delusion, Shamelessness, Fearlessness, Restlessness and having clinging-object which receive via 6 doors by contact, feeling, perception, intention, one-pointedness, life, attention, thinking, keeping thinking, decision, keeping trying, (sometime maybe conceit or wrong view or Sloth (mind) and torpor (body)).

But the right view can't arise with above factors. The right view must arise with wholesome Nama.

sobhana-sadharana cetasika (Beautiful Ones - 19 which arise with all whole some mind)

1. saddha = faith, confidence
2. sati = mindfulness, attentiveness
3. hiri = moral shame
4. ottappa = moral dread
5. alobha = non-attachment, greedlessness, generosity
6. adosa = hatelessness, goodwill
7. tatramajjhattata = equanimity, mental balance
8. kaya-passaddhi = tranquility of mental concomitants
9. citta-passaddhi = tranquility of consciousness
10. kaya-lahuta = agility or lightness of mental concomitants
11. citta-lahuta = agility or lightness of consciousness
12. kaya-muduta = elasticity of mental concomitants
13. citta-muduta = elasticity of consciousness
14. kaya-kammannata = adaptability of mental concomitants
15. citta-kammannata = adaptability of consciousness
16. kaya-pagunnata = proficiency of mental concomitants
17. citta-pagunnata = proficiency of consciousness
18. kayujjukata = uprightness of mental concomitants
19. cittujjukata = uprightness of consciousness

virati cetasika (Abstinences - 3)

1. samma-vacca = right speech
2. samma-kammanta = right action
3. samma-ajiva = right livelihood

appamanna cetasika (Illimitables - 2)

1. karuna = compassion
2. mudita = sympathetic joy

pannindriya (1)

1. pannindriya = wisdom or insight

1.phassa = contact or mental impression 2.vedana = feeling 3.sanna = perception 4.cetana = volition or intention 5.ekaggata = one – pointedness, concentration (samadhi) 6.jivitindriya = vitality or psychic life 7.manasikara = attention or advertence

1.vitakka = initial application or thought conception 2.vicara = sustained application or discursive thinking 3.adhimokkha = decision or determination 4.viriya = effort or energy or exertion 5.piti = rapture or interest 6.chanda = wish, desire or will

So, you can notice the difference of your mind by analysis it's factors. However, it is hard for people who have no skill in wholesome meditation especially concentration meditation because it is the base of soft analysis (first step of the insight meditation).

See https://www.bdcu.org.au/bddronline/bddr12no5/bddr12no5.html

Is the “right view” as described in the Noble Eightfold Path the same kind of “view” that is described in Snp 4.5?

Yes.

If so, does this mean that a Realized One abandons a profound universal truth which is true whether a Realized One arises or not??

If not, then what is a “view” as described in Snp 4.5 and how is it different from the “right view” of the Noble Eightfold path?

Yes, in meaning "abandons clinging on a profound universal truth".

No, in meaning "thinking of a profound universal truth".

The noble one can know both wrong view and right view, but they understand the truth of them without addict, clinging, craving on the wrong view.

To analysis them see above factor list to analysis each mind whether wholesome or unwholesome by checking it's factors.

Also, the Buddha often described things with the adjective “foremost”; does this mean those things so described were not “views” as meant in Snp 4.5?

It is about 4 bias. When one is clinging on a view and deny other views without understanding the truth, they may decide the right as wrong.

For the example, one decide to cling whether "there is no next life" only, but if it is possible, he miss the truth. Or one decide to cling whether "there must be next life" only, but if it is impossible, he miss the truth. Then when they meet each other, they will argue and fight each other "all me right, all you wrong" without trying to understand the truth.

This is basic explanation. It is more very complex and advance for the insight meditation. We study and practice each mind moment in trillion times arising per second whether "which is wholesome? which is unwholesome? Which is 3 characteristics". And for this very big data analysis, we practice advance concentration meditation.

"Monks, I will teach you the Dhamma compared to a raft, for the purpose of crossing over, not for the purpose of holding onto. Listen & pay close attention. I will speak."

"And what should the man do in order to be doing what should be done with the raft? There is the case where the man, having crossed over, would think, 'How useful this raft has been to me! For it was in dependence on this raft that, making an effort with my hands & feet, I have crossed over to safety on the further shore. Why don't I, having dragged it on dry land or sinking it in the water, go wherever I like?' In doing this, he would be doing what should be done with the raft. In the same way, monks, I have taught the Dhamma compared to a raft, for the purpose of crossing over, not for the purpose of holding onto. Understanding the Dhamma as taught compared to a raft, you should let go even of Dhammas, to say nothing of non-Dhammas."

• MN 22

The noble eightfold path is a fabrication. The arahant has gone beyond. But he might still use it as its evident from this sutta :

"Then which things should an arahant attend to in an appropriate way?"

"An arahant should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. Although, for an arahant, there is nothing further to do, and nothing to add to what has been done, still these things — when developed & pursued — lead both to a pleasant abiding in the here-&-now and to mindfulness & alertness."

Snp 4.5 is describing someone who has gone beyond :

A brahman not led

by habits or practices,

gone to the beyond

—Such—

doesn’t fall back.

Even today, in English, there are two distinctly different, even opposite meanings of the word "view". In one view we see with our eyes -- in other words, gaining direct knowledge through an experience. In the other view we see only with our mind's eye -- in other words we think something. The first is literal, the second uses the literal as a metaphor to describe something figurative. I would suggest that the suttas you cite are using the word diṭṭhi in the same way.

It is possible for the second kind of view to equate to the first. We can see, with the mind's eye, something we have experienced directly. If we literally saw something, we later have it in mind. Or maybe we literally felt something or tasted something -- still direct knowledge -- and later we imagine that experience. In all those cases we would still have the first kind of view, drawn from direct experience, as long as we don't overlay the experience with opinions about it.

It is also possible for the second kind of view to have no equating to the first kind. In this case we can also call it 'an opinion'. It is not based on actual direct experience, but it is based on imagination alone, concocted from things others tell us, or what we have read, or -- as in the Kalama Sutta -- what seems logical to us, or even what our teacher told us.

by reports, by legends, by traditions, by scripture, by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by the thought, "This contemplative is our teacher."

The "right view" of the path is the first kind: drawn from direct experience. The "view" in Snp 4.5 is the second kind: an opinion. It is easily distinguished by the sign the Buddha provides in the lines you quoted: the holder of the view tells others their opinions are low, and those views result in disputes.

But also note that, according to MN 117, there is more than one kind of "right view":

And what is right view? Right view, I tell you, is of two sorts: There is right view with effluents, siding with merit, resulting in acquisitions [of becoming]; there is right view that is noble, without effluents, transcendent, a factor of the path.

As for "the foremost" I think we might need examples of suttas where you think the term might relate to "views".