100% of your reply is incorrect.
I don't believe this and what I gave was just an example--but an example that exemplifies my point. Namely, that a foundation in an area that requires careful manipulation and understanding of evidence to arrive at true conclusions is broadly useful in less rigorous and more broad contexts. I believe that--all other factors being equal--your average scientist in a mathematical field has a greater capacity to discern truth (and understand the relevant context) than people with a similar amount of education in other areas.
I think your statement needs more critical thinking too, because at no point did I mention proving all statements--in fact, good luck even figuring out how to state anything you might want to prove in a proof assistant; that's often harder than the proof itself. (It's actually even more limited--you can only prove propositions with computable proofs.)
In my decade of university education, I have never had a professor mention any personal political beliefs in a lecture and I attended schools far more liberal than UT. It's funny you qualify this with "liberal"--would you be more at ease with conservative professors pushing their ideology on students?