Two contradictory passages in the Majjhima Nikaya

There is no contradiction. The raft simile is about not engaging in "gahaṇa".

In the same way, I have taught how the teaching is similar to a raft: it’s for crossing over, not for holding on.

Evameva kho, bhikkhave, kullūpamo mayā dhammo desito nittharaṇatthāya, no gahaṇatthāya.

By understanding the simile of the raft, you will even give up the teachings, let alone what is against the teachings.

Kullūpamaṁ vo, bhikkhave, dhammaṁ desitaṁ, ājānantehi dhammāpi vo pahātabbā pageva adhammā.

gahaṇa

neuter

seizing, taking hold of; grasping; grasp: acquiring

For example, the Vinaya uses the term "gahaṇa" in relation to a man lustfully holding the body of a consenting nun (woman).

Therefore, when MN 22 says to 'pahātabbā' ('cast away'; 'give up'), this refers to casting away 'gahaṇa' of the teachings (rather than say faith in or reverence for the teachings).

Keep in mind MN 22 is about the simile of the snake rather than about the simile of the raft. The purpose of the simile of the raft is to explain the simile of the snake, namely, to memorize the teaching for the sake of finding fault and winning debates.

Therefore, when MN 22 says to use the raft properly, this means to not use the raft for the sake of finding fault and winning debates.

As for MN 88, the term is 'samannāgata', which means 'endowed with', as follows from MN 117:

So the trainee is endowed with eight factors, while the perfected one is endowed with ten factors.

Iti kho, bhikkhave, aṭṭhaṅgasamannāgato sekkho, dasaṅgasamannāgato arahā hoti.

I think some people say that the parable of the raft is about giving up the Teaching -- or as it seems to be phrased in the question, "relinquishing what is skilful" -- but I don't read it that way.

In context:

• The monk Arittha has a wrong view
• Other monks try to dissuade him and fail
• The Buddha reproves him, and gives the parable of the Water-snake and of the Raft.

In my opinion the water-snake parable says, "If you grasp it improperly then it will harm you".

And similarly the raft: that it's wrong to hold it for too long.

But I don't think that's saying -- or at least I'm not sure that it's saying -- "abandon the teaching" ... which a lot of other people seem to say.

Instead I think it's like the water-snake parable, i.e. "don't grasp it wrong", or in this case maybe, "don't take it too far", or "don't stretch the analogy beyond its intended context".

To double-check my theory -- only sensible if other people contradict it -- I look at Piya Tan's analysis. That somewhat supports my theory -- on what it calls page 55 (which is page 6 of the PDF)

In the parable of the raft which is the key parable here—the Buddha goes on to show the serious error that lies in wrongly grasping that which one has learnt, that is, the dangers of misconceiving and misinterpreting the teaching

That's paraphrasing Gombrich according to the footnote.

On page 56:

As such, we can see that Buddhaghosa takes part (2) of the Sutta as the core parable, and the other parts as giving its meaning. Thus, Buddhaghosa clearly sees the Alagaddûpama Sutta through the parable of the water-snake, as addressing the dangers of wrongly grasping the dharmas (truths and teachings).

Then on page 57 he says, which seems to contradict my theory,

While the Pārājika 1 story stresses the letting go of sexuality, the Sutta stresses letting go of the Dharma itself before we can progress to self-awakening. Hence, it is very clear why the Buddha declares that, having understood the parable of the raft [§13], “you should abandon even the dharmas, how much more so that which are not-dharmas” (dhammā pi vo pahātabbā pag’eva adhammā) [§14]: in simple terms, we should abandon even right views, what more of wrong views.

It then goes on the say that "Dhamma" is a word of many meanings, and then for example:

Once again we have a deceptively simple term (dhammā) whose context is very clear. If we take dhamma here, without any Abhidhamma technicality, as simply meaning “a state that is occurring, a present mental event,” then the Buddha’s import is very clear. He is advising us to be mindful of the nature of mental states and sense-experiences as they arise.

And this is his conclusion on page 60:

The context here is that of interdependent arising (paṭicca,samuppāda), that is, a doctrine. It is thus clear that the meaning of the parable of the raft is

that one should not become slavishly attached to a view even when that view is true. One should understand the true nature of consciousness but not become fixated on it qua philosophical theory. It must be put to its proper use as part of the Path and within the context of the rest of Buddhist teachings.

... and:

Gombrich goes on to say that the Buddha is himself aware of the dangers (or disadvantages) of “putting words first” (pada,parama), that is, the last of the four types of unawakened learners.

In MN 22, the term "Dhamma" in the context of the raft simile refers to "the teachings" (based on the context of the sutta), and not to "phenomena" or "mental objects/ phenomena".

In the quoted statement of MN 88, the term "dhamma" refers to "mental objects/ phenomena", and not to "the teachings".

So your question is similar to saying "you can eat turkey" and "you cannot eat Turkey" as contradictory statements.

Dhamma is an explanatory device, a discursive construct meant to make a point. Understanding the point you get what it refers to in your immediate experience. Then you can cultivate and eventually actualize or realize the wholesome "states", e.g. non-grasping.

The wholesome states exist in the realm of experience while the teaching exist in the realm of theory. The teaching is a model or a schematic and being schematic it is a crude approximation. Because it's a crude approximation, taking it literally and obsessing with its literal meaning is an obstacle to achieving the wholesome states in practice.

Attaining the wholesome states requires going beyond the schematic and into the experiential.

This is why there's no contradiction there. You abandon the raft - going beyond the schematic - and this is exactly the final stage of actualizing the wholesome states.