Identity politics is inconsistent because it promotes a notion of identity that aligns entirely with selfhood - what someone feels themselves to be. I know I've said this before, but my problem with identity politics lies in the way it transforms identity into a metaphysical presence, something that corresponds an internal sense of self rather than an external set of conditions.
That's all well and good, sure, whatever - I don't believe in identity as a metaphysical presence, or that it corresponds to some internal selfhood, or that it's as easy as simply "choosing"... but whatever. More power to them. Except that identity politics runs into a glaring problem when it comes to racial difference, and that is that someone can't will away racial discrimination by internally identifying as "white." It's much easier to pass as straight than it is to pass as white (obviously, people shouldn't have to "pass" one way or another, people should be able to express themselves... but still, it happens to be the case).
Now, second issue: while queer people absolutely experience bigotry, the experience of being queer isn't aligned historically or culturally with economic disparity, as is the case with African Americans (largely due to slavery I say, but let's not get into that again). So, identity politics emerged en force primarily among a group of generally economically privileged/entitled individuals, as being gay did not necessarily prevent you from getting a job, the way being black might.
So, identity politics became a contemporary narrative of metaphysical identity that promoted the liberal expression of selfhood, of who we "really" are inside; and this radically conflicts with Marxist notions of identity as determined economically and socially. Black people don't have the privilege of avoiding discrimination by "choosing," and their history of discrimination and exploitation isn't wrapped up in what identity they chose for themselves. So, when it comes to race relations, Marxism and historicism were the primary touchstones for a long time because they addressed the material (i.e. external, we could say) dynamics of race relations, the way that racial identity is something produced by exterior phenomena (skin color, dialect, physiognomy, etc.). When identity politics came along and coopted race relations, it introduced an intersectional quandary that's seeing its effects in cases like Rachel Dolezal (although she's a rarity, she's emblematic of the contradiction at the core of identity politics).
Also for the record, and to plug my own field of study: This is why we see strikingly imagined fantasies in black literature like George Schuyler's Black No More, which imagines the invention of a machine that can change black skin white (the story is a satire, and it's incredible). Schuyler's book can be read as a critique of identity politics, and it was published in fucking 1931.