At some point you might realize that you're just thinking about empty labels that you fill with stuff that makes you feel better.
I wouldn't disagree with that, but the author in question doesn't seem to follow that line of thinking so it seems irrelevant here.
But this doesn't mean I can't read something that has been written still using the word "conservative" as a lazy synonym for Republican, suspend my particular frustration about the terminology, and understand the point the author is making.
These two words lend themselves to that, because of what we use them for. I would not reject them, though. Naming things remains useful; and whatever words we would replace these 2 with, and we would, out of necessity: they'd receive the same treatment.
The words are not the problem here. Using them without thinking is.