YU and YCT both teach Tanach and Machshava.
Dr. Hall: WADR, Colleges are supposed to teach philosophy and “Bible studies”. IIRC, CUNY schools teach Tanach & “Machshava” as well.
The question is if it is taught in high school/college as a Limud, or as a subject. It is certainly more common to learn Nach as a “history” subject.
I can’t speak for YCT, as I know nothing about it. I would think though that they are an exception, rather than the rule, to “Modern” or “centrist” Yiddishkeit.