What should we accept? What should we let go?

You should accept The Eightfold Noble Path:

1. Right view
2. Right resolve
3. Right speech
4. Right action
5. Right livelihood
6. Right effort
7. Right mindfulness
8. Right Concentration

Everything that goes against that, should be rejected. FYI, The Eightfold Yoga System has the same injunctions. In Yoga, the first two steps are called yama (that what should be accepted) and niyama (that what should be rejected).

And what is right effort? It’s when a mendicant generates enthusiasm, tries, makes an effort, exerts the mind, and strives so that bad, unskillful qualities don’t arise. They generate enthusiasm, try, make an effort, exert the mind, and strive so that bad, unskillful qualities that have arisen are given up. They generate enthusiasm, try, make an effort, exert the mind, and strive so that skillful qualities that have not arisen do arise. They generate enthusiasm, try, make an effort, exert the mind, and strive so that skillful qualities that have arisen remain, are not lost, but increase, mature, and are fulfilled by development. This is called right effort.

https://suttacentral.net/sn45.8/en/bodhi

What should we accept? What should we let go?

Every evil never doing
and in wholesomeness increasing
and one's heart well-purifying:
this is the Buddhas' Sasana

(Dhammapada, 183)

I am not sure there is a difference between letting go and acceptance ,If there is a let go ,there has already been acceptance.And its not directed towards anything specific, its basically all that manifests, everything including the sense of a self that needs to accept and let go.

Expressed well here in the Na Tumhaka Sutta

I am not going to quote a sutra, but I am trying to let go of everything, including letting go. :)

What is it to let go in Buddhism?

Is that the Noble Truths?

So

1. recognise suffering
2. associate that with (recognise that as arising with) craving and attaching
3. let go

It's also a past-tense, is it, i.e. -- "suffering having been known in the past, it was dropped".

What is it to accept in Buddhism?

I'm not sure it is -- does acceptance imply a specific view of a specific "thing" accepted (which may be contrary to the doctine of things being empty), also of a "me" doing the accepting?

Realistically, though, maybe monks accept what "necessary" (i.e. the "requisites").

There's also conventional wisdom (to be accepted) -- like from here:

And what is wrong view?

'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.'

This is wrong view...

So an excess of "nothing exists" is wrong too.

So I suppose that "accepting" in Buddhism is, at least, not rejecting being kind and so on.

What are the things we accept?

Should accept good advice, probably.

What are the things we let go?

Bad habits. And heedlessness.

Why? How?

Liberation from suffering -- personal welfare and the welfare of others.

Accept the truth; all created things are impermanent, all created things are not self.

Let go of what is not yours, the stress & ill.

The semantics of acceptance and letting go of things are fairly mundane.

However the term letting go appears in texts in not so mundane context like; 'eye is not yours, let go of it' the relinquishment of the clinging based on misconception about 'the eye' is what is referred to as i understand it.

Letting go is talked about as a release in the general sense of releasing as in letting something go and disconnecting, ie;

"And this, monks, is the noble truth of the cessation of stress: the remainderless fading & cessation, renunciation, relinquishment, release, & letting go of that very craving."