I'm sure that applies to a good chunk of the population, but I think there's more to "no war but class war" than just dodging personal responsibility.

The owning class needs to convince people to vote against their best interests, and the primary tactic they use is to divide the working class.

"If you can convince the lowest white man he's better than the best colored man, he won't notice you're picking his pocket. Hell, give him somebody to look down on, and he'll empty his pockets for you."

Would winning the class war fix everything else? Hell nah - the rich aren't just making these divisions up. But they are going to do their best to stoke the flames, because they need the distraction. We need to fight patriarchy no matter what. But the class war is making those fights harder.

All that said, trying to downplay legitimate concerns about oppressed populations by saying "no war but the class war" is very "all lives matter".