Identity's a bit like the communist using an iphone thing.
We can rail all we like about people basing some or even all of their activism and/or political awareness around identity but the truth remains that identity is a part of how we experience the world. A lot of that is down to how capitalism constructs us, and how we construct ourselves in response to it, but it's perfectly possible—in fact necessary—to recognise the relationship between capitalism (and class) and identities, to be critical of that relationship, and work in ways that take account of how we live within that system. Identity is a reality. That it's constructed doesn't make it any less real.
And the thing about class as an identity: class is a system first and foremost, but it is
also an identity because of the way it has been constructed as one. The problem comes when the idea of it as an identity supplants the understanding of it as a system, and it requires constant work to keep grounding it in those terms.
But one thing I think a lot of class-aware people do is think everyone who is engaging in any kind of progressive or leftwing politics should be 100% up to speed the moment they begin. It doesn't work like that. I spend time on tumblr. I've said before, over the years I've seen a distinct shift from solely 'identity politics' (of which there are various types, some far more conscious than others), towards class awareness. In some cases that class aspect is treated like another string of identity politics, but there are also good conversations discussing it in ways even the staunchest of gits on here would approve of. In large part that's been fuelled by Bernie Sanders' popularity, the rise of the DSA, and a subsection of more visible socialists and communists on social media (many of whom are people of colour). I feel largely positive about tumblr, because while there's a fuckton of absolute shite, it's also exposing a huge number of teens and young adults to leftwing politics that, sure, doesn't always have a perfect analysis but is the beginning of a journey.
(I'm aware Sanders etc seats this in American politics, but when we talk about identity politics it's impossible to ignore the influence of American politics.)