It could be partly that "identity" politics are based on things you can't change, your race, your sex, your sexuality etc. But you can have a certain level of control over your class. Varying levels depending on where you live and the economic system you live under of course. But poor people can and do become rich. It's not common, and not achievable for many, but to claim it never happens or that the "bourgeoisie" and the "proletariat" are immutable categories (as many Marxists do) would be untrue. So that's to me why class isn't included as an identity when all the other "isms" are.

“The nature of our immortal lives is in the consequences of our words and deeds” — Cloud Atlas

“The nature of our immortal lives is in the consequences of our words and deeds” — Cloud Atlas