In my experience on and offline, socialists, social democrats and liberals alike have largely bought into the whole identity politics way of thinking about oppression, and the right has also happily lapped it up in the UK.
And there are some socialists, social democrats, liberals and right wing folks who see it for the bullshit that it is, but the issue is that the left is meant to apply class analysis to how we understand power structures, we are meant to reject individualism. In other words you would expect identity politics to be embraced by the non-religious right and many liberals precisely because it abandons dismantling power and instead upholds personal identity in a way where oppression is simply understood as a points system denoting who should be silenced and who shouldn't, as I say allowing those power structures to remain entrenched and largely unchallenged. As Tanitha said in the video, identity politics is ultimately a victory for capitalism.
So the bottom line is that the left is where this should not be happening, and the fact that it is is an abandonment of leftist politics. And the authoritarianism of the left, which again is something embraced across the left to quite a degree, compounds this problem by using identity politics as a means of restricting free speech, something the right is not doing. So I think it is very important we understand what is going on, as it helps us to challenge it. I've had countless conversations with others on the left who support identity politics. None of them can defend that support in a leftist context. I think Tanitha's video is great at exposing why....