University of Tulsa (local to me) is nominally associated with the Presbyterian Church but has no overt religious presence. My kid, who eliminated both St Olaf and Southern Methodist University as too religiously affiliated, considers TU to be acceptably secular.
I do think of it as being on the conservative end of the college campus spectrum, but more due to political apathy and an engineering-and-business preprofessionalism than for religious or ideological reasons.