Sure. The Culture War’s belligerents are all, generally speaking, illiberal. And notably, most people steeped in it reject the term. Even those on the left.
So what are they supposed to do then. The right makes a mountain out of a molehill. That happens to target some group, like a minority. Those on the left who reject the Culture War argue against it since they think the right’s focus will hurt the minority. They argue that the right is making a mountain out of a molehill. And yet they are now participating, begrudgingly.
Self-identification is confused enough but identifying others is even more muddled.