Plenty of private Liberal Arts institutions are liberal to the point of caricature. Plenty are more "traditional" aka reflective of wealthy conservative values. All are populated by the ultra-wealthy in general, so often the outward appearance of humanistic, progressive values simply serve to cloak a cold, corporate soul.
As far as public universities go, yeah, much of the faculty - hyper-educated, comfortable though not necessarily rich - skew left, particularly in the humanities. But where public, state funds are involved the politicians exert a lot of influence on University policy. It couldn't be a more bureaucratic, bottom-line system. In Iowa, for example, the University faculty have been fighting (to no avail) against the appointment of a complete hack from the business sector to the school presidency. This can be traced back to the board of regents, who are appointed by the governor, who is friends with the Koch brothers. Our nation as a whole is extremely conservative and corporate-minded - what passes as the democratic agenda today would've made conservatives blush in previous decades; what passes for republican thought would've been considered sheer lunacy by conservatives in previous decades. As much as people bandy about the terms "oligarchy" and "plutocracy" it's clear they don't quite grasp just how serious, present, and dangerous the corporate takeover of America is on just about every level of public life. The Trans-Pacific Partnership should scare 90% of the populace to fukking death. But no one has the time or information or critical skills to know what the fukk it even is. And that's the point of the new University model - to keep people focused on becoming cogs, and not view our culture critically.