The problem with identity politics is pretty simple.

You start with the, correct, observation that different "identities" ie. races, genres, sexualities etc etc. get to experience the world in radically different ways, usually because they are somehow different from the norms of the culture / society in which they live.

And the purpose of identity politics is to resist / deal with that by ...

Well, that is where a fundamental dilemma or bifurcation point appears.

On the one hand, you can respond by denying that there IS a real, fundamental difference. That the purported differences are simply due to errors of, or prejudices of, or categories constructed within the power-structures of, the society and its dominant identity.

The challenge, therefore, is to overcome these prejudices and constructed categories for the identity to be recognised as the same, and to be allowed to be able to participate in society as peers and equals to the dominant identity.

On the other hand, you can accept that there is a difference, and instead claim that the values or ways of being of the identity you are fighting for, are better than the values of the mainstream dominant identities. And should therefore be valorized or adopted. Perhaps should even supplant those of the mainstream.

We'll call this first group and first politics, the "same and equal" position. And the second, the "different but better" position.

Now these are fundamentally different and opposed political viewpoints and projects. But the tendency in new identity movements is to ignore or gloss-over the distinction. Advocates of an identity politics will often feel uncomfortable with, and deny, that there two contradictory projects. Many activists will respond to and accept beliefs from both positions. The distinction will not be worth trying to enquire too deeply into or firm up.

Nevertheless, as far as I can see, almost all the problems that arise in identity politics : the internal quarrels and ruptures, often turning into bitter and vicious civil wars, or even just debilitating quarrels about "strategy", often stem from not recognising this distinction, and then discovering it in the context of a particular policy difference around which the two camps do then split, often bitterly.