Thanks for posting the full set of rules. The only thing that's vague (and could be read as violating the new Texas law) is the "no coming to campus without authorization." The law makes it clear -- EVERYONE is "authorized" to be on the public spaces of all state university campuses. It may be enforceable to issue trespass warnings and prohibitions against certain individuals based on specific events, but then the rule should say "coming on to campus when entry has been legally prohibited."
1) there are still ways to handle violations of said rules. Foremost, only take action against the actual INDIVIDUALS violating said rules. If it's Jane's tent, then clear out Jane and her tent. If Jim is wearing a mask and refuses to remove it, remove Jim. You don't get to "punish" the entire group for individual violations.
2) they can't charge or require "permits" (the statute our governor was so excited to sign....when he thought it was only to protect right-wing speech....says exactly that). I think there CAN be a "permit" or "pre-clearance" process that is voluntary, and that the university can ask people to follow in order to help protect the university, the free speech process, and the demonstrators (e.g., if the subject of a demonstration is likely to draw a counter-demonstration, and maybe have a heightened risk of violence, it's good to give UT a heads-up so they can be on guard against shenanigans that could harm any protestors).
None of this shit is in play, though. UT is going full-on heavy handed jackboots because that's the message the university wants to send.....when the message is not one the governor favors.