The problem with being "anti-woke" is that "anti-woke" now represents an extreme absolutist ideology that has become prominent on the political right.

So it's better to adopt a different brand. I am an anti-illiberalist in practice, for instance. (My ideological commitment to this is fairly weak, but pragmatically it seems warranted given the nature of the primary contemporary challenges to liberalism.) I wouldn't mind saying so. Wait, I just did say so. So, there you go!

I do mind, at this point (though not a couple years ago) characterizing myself anti-woke, however, because the extreme absolutist ideology on the right has co-opted the label to too great an extent.

I advise you to think more deeply about TaraElla's points here, and also, if you haven't already, read some of her other stories about the "anti-woke" yet still postmodern and illiberal right.

It's not that occasionally supporting the right is not okay--as John McLaughlin used to say (but about someone on the left), they occasionally stumble uncontrollably into the truth. However, supporting the illiberal postmodern and now "anti-woke" part of the right is not okay.