I think that's not the only reason, sometimes not a reason at all.
Instead, 1, sometimes, someone is looking to make a career, or get a job, make money. And then, in identity politics, they might see an opportunity. Career, status, money then being a goal, and any division a side effect.
And, 2, I'm not saying that identity politics is or would always be bad or anything like that. So many unfairness in the world, to try to correct.
Well, it's a newish power niche that's getting exploited.
(One (postmodern) interpretation is that it's yet another "society of control" in crisis. Basically, the old tools that provided stability (social conventions, morals, beliefs/prejudices) all used to look like big formalish institutions, from family-school-factory-military-prison, and you were either in the system or completely out of it. But as this system of systems post-WWII has "eaten the world" it's now bound to face its own limitations, hence the crisis. Hence all the reforms, real and so-called ones.)
The niche is (was) that most people has (had) only a super basic over-simplistic belief about language, which could be summed up as "something something the n-word". Instead of the more correct "when talking to/about someone it's very disrespectful to call them names they don't like".
In general, creating division between classes, races, religious groups presents opportunities for individuals to gather power by taking up the cause for one group. By establishing an “other” you have an enemy to rally support for your leadership. This is the basis of power for every demagogue from the Cleon in Athens to Joe McCarthy and the American Red Scare. This is also a core theme in Orwell’s 1984.
In the context of the OPs topic, there are those who honestly are trying to improve the world, but many people have new found careers and political power created by the division on both the Right and Left.
I mean, this sets off my satire alarms but wouldn't that be a worthy goal? We can cynically deride all attempts to connect humanity as worthless hippy mumbo jumbo, and while I think perfect adherence would be impossible, I think a step or two in that direction is both possible and beneficial for us. This cynical attitude (assuming satire) is exactly the type of thing preventing us from making that kind of progress.
Call me a cynic but I am all for that. And afterwards you encounter the flat earthers and the holocaust deniers and the Putins and Alex Jones of the world and all kinds of other extremists in all kinds of extremes of all directions. And then it's not so simple.
While partially true, what most fail to see is that identity politics is played by virtually everyone. It’s just “your” side is the right approach and “not really identity politics”.
Identity politics has been the bedrock of American politics since before the Mayflower Pilgrims[1] landed at Plymouth rock, and hasn't ever stopped for even a day. Any claims of recency says a lot about the speaker rather than reality.
1. That they were "pilgrims" is enough evidence. All the jey moments in American history are underpinned by "identity politics": the the 13 colonies, manifest destiny, expansinf west, the declaration of independence, slavery, civil war, reconstruction - all of it.