The short answer is that yes it's very different (contrary to other opinions). Although still liberal (by Harvard/Yale standards), UCLA/Caltech don't even compare to Stanford/Berkeley. LA is also much more cosmopolitan, so you'll naturally get a more varied distribution of ideas on the political spectrum.

I would argue that for the most salient issues of our time, UCLA, Berkeley, Stanford, Hopkins, et al, will all support sufficiently liberal social and political policies that from the outside perspective all look the same. Sure, a few colleges may really demonstrate its history of activism.

But which top college wouldn't culturally or administratively have a positive atmosphere towards immigrants, financially disadvantaged, Muslims, gays, sexual equality, or gender issues? Basically the salient topics of our time.

Peter Thiel might simply want to take advantage of the less-crowded LA tech scene, or I suspect he might've tried Austin, but even then, I don't think it's that much different in atmosphere.

It's not just about left/right.

Compared to SF, LA is a true big city, as close to New York as you can get on the west coast. In comparison SF is a petty small town, complete with the provincial backstabbing and all.

no "provincial" backstabbing in LA/NYC - God no.

No

Although Breitbart is headquartered there, so I’m sure he will find some conservative friends.