Baylor U. is “Baptist” like Notre Dame is “Catholic”.
I have a daughter who went to Baylor Law School (she has since transferred to the University of Alabama chasing a boyfriend, not because she did not love Baylor). She went to UNC for her undergraduate work. In relative terms, Baylor is quite conservative when compared with UNC. Alabama is just as conservative. I suspect that the faculty at Baylor is much more liberal than the general Texas population, but pretty conservative when compared with most college faculty.
It seems that there is probably more political diversity among departments at individual schools than between the schools themselves. For instance, I went to Wake Forest Law School in the late 1970s. At the time, that law school faculty was infamous for its libertarian views. That experience affected my views a great deal and I am mostly libertarian today. Most engineering and business school departments have more than their share of conservative/libertarian faculty members. Most political science departments are bereft of conservatives or libertarians.
I would not worry too much about the political bent of the school, particularly as an undergraduate. Send your kids to a school with a challenging program that insists that they take core courses that actually mean something or tell your kids in no uncertain terms that you will fund a broad liberal arts education that requires thought or that they can find the money to fund themselves.
Two choices that are not in Texas, but are worthwhile are the U. S. Military Academy and the U. S. Naval Academy. Kids get a good education and the Academies build character.
Two other schools are particularly interesting. One is St. John’s with campuses in Annapolis, MD and somewhere in either New Mexico or Arizona. The other is The University of the South (a/k/a Sewanee) in Sewanee, Tennessee.
St. John’s has a unique view of education that is worth while. Students are required to take two years of Latin and two years of Greek. They read original works and not text books about them. For instance, they use Newton’s Principia (sp?) instead of a calculus text book.
Sewanee offers a fine liberal arts education in what is certainly the prettiest place I have ever seen. More impressive is that no one needs to lock up their bicycles and most folks do not lock their doors. If your kids have any athletic ability they can probably play on some Sewanee varsity team. Sewanee has a huge number of Rhodes Scholars on a per capitia basis. The student body is quite conservative. It is an Episcopal school, but it turns out some pretty conservative Episcopal priests.
Having said all of that, my kids all applied to Sewanee and all got in, but one went to Wake Forest, one went to UNC and one went to North Carolina State for their undergraduate work. Sewanee was the strong second choice for all three of them. None was interested enouth in the St. John’s program to apply, although one spent a weekend at the school.
All three of my kids are conservative with libertarian tones. One could probably be better described as libertarian with conservative tones.