UT is basically considered a very liberal/left leaning campus, but that is probably because the nutcase professors get the most media attention. The University is so large that your daughter can pick and choose with whom she wants to associate. I do know that they have a large, active Young Republicans club on campus. I've met quite a few of these kids, and find them very impressive.
Mainly, it will be up to your daughter to make the choices that are right for her. Having been raised in NJ--UT will probably seem ultra conservative to her--LOL!
If you would like and think it would be helpful, I'll be happy to give you my telephone number to pass on to her in case she thinks I might be helpful to her in any way. It might be good for her to have a local contact of the adult persuasion (grin).
And, of course, when you come to visit, I'd love to meet you.
That's what I liked about UT--it's HUGE--so she can find anything that suits her there. She already expressed interest in joining the Young Republicans. I raised her as a conservative first and a pubby second (she is well aware of the saying "I vote Republican to stop the Democrats").
She wanted a big university, and I figured that although you cannot escape the libs on any campus, UT would have a bit of a more conservative bent.
Next time I'm down there let's all try and get together for some texmex or ribs. I look forward to meeting you (and, I am a Lifetime NRA member since 1975, so I love the fact that you are a charter member of the Second Amendment Sisters).