Yeah looking at the meme it definitely misuses the saying “no war but class war”. People in the comments are pretty unanimously taking it as OP did, probably because they are viewing it not only as a rightwing psy op but foremost as a material attack on their civil rights (which is indeed what it is.) if you intended to dismiss the ‘culture war’ as a right wing op then this missed the mark because it didnt take the mask off to reveal what the culture war actually is - it just dismisses it in favor of class war (which is a false choice) and somehow legitimizes the culture war by applying it as the target of an antiwar slogan.

In summary the meme is bad. It doesn’t reflect your stated views, it acknowledges the culture war as a war, and then makes a point not to participate in that and to focus on class instead.