As I've noted before, public universities have considerable authority to impose content-neutral rules on demonstrations, for instance prohibiting overnight campouts, restricting sound amplification, and so on. But of course the First Amendment requires such rules to be content-neutral (or, in "limited public forums" on campuses, at least viewpoint-neutral). And even content-neutral restrictions in outdoor quads, at least as to student gatherings, still have to be reasonable (to oversimplify the rules slightly).
Beyond that, a 2019 Texas statute reinforces this, and indeed provides even broader protection than the First Amendment minimum. In particular, it treats "outdoor areas of the institution's campus" as tantamount to "traditional public forums," open to all members of the public. This designation also precludes content-based restrictions. (Some public universities might be able to argue that such outdoor spaces are only "limited public forums," where content-based but viewpoint-neutral restrictions are allowed; not so in Texas.) And it provides that restrictions must be "narrowly tailored to serve a significant institutional interest" and must "leave open ample alternative channels." (Again, if a university could treat an outdoor space as a "limited public forum," restrictions would only need to be reasonable; but in Texas the bar is higher.) And the statute "recogniz[es] freedom of speech and assembly as central to the mission of institutions of higher education."
This makes me pretty skeptical about the dispersing of protesters at UT. First, Governor Abbott's statements suggest that this happened because the protesters' speech was anti-Semitic; but that's a viewpoint-based basis for restriction, not a content- and viewpoint-neutral one. (The Governor appears to have been involved in the police actions here.) Second, from the press accounts that I had seen the protesters appear to not have been engaged in sleepouts, blockages, or other things that violated campus rules; and to the extent that they didn't have a permit, there seemed to have been no "clear, published, content-neutral, and viewpoint-neutral criteria" (to quote the Texas statute) justifying any denial of a permit.
