Given the contexts I most commonly see it used in, I think it means “having empathy for someone outside my identity group”.
It's anti-White, Europhobic, misandry, etc.
So much for "having empathy for someone outside my identity group".
Given that many such comments also amount to gaslighting, that's what bothers people about the whole idea. It was a good experiment, but it's time to end the policies and the attitude it brings. There are better things to argue over, this isn't one of them.