But the issue here is not ideology, it is the fact that things like "Gender Studies" aren't part of the liberal arts at all. It's the fact that these "special interest" degrees are ideology, lol. All DeSantis is trying to do is get rid of the ideology in education, and this is badly needed.
Jonathan Haidt--who is historically liberal--writes a fair bit on this problem through his Heterodox Academy, but also elsewhere. I am pulling from memory, but his basic distinction is that some universities are about truth and some are about change. The classical, liberal arts model, is about truth. The "critical studies" degrees are about change.* Their express purpose is to bring about a particular change in the world, and this is where Rob's point becomes particularly salient. Why should taxpayers fund public institutions which exist to promote changes they feel to be undesirable? That's a great question. Another is, "Why is public money being spent for the sake of (ideological) change at all?"
The "Gender Studies" department of a university is essentially a political special interest group, or a partisan think tank. In the American scheme such institutions are necessarily private, and this is because public funding aims to further things which are non-partisan. And we do have private colleges and universities which devote themselves entirely to critical studies or women's studies, and that's fine. They are functioning as a sort of private think tank and special interest group. The problem is when the government itself begins endorsing and funding such partisan initiatives.
* Think of Marx's famous quote, "The philosophers have hitherto only interpreted the world in various ways. The point, however, is to change it."