It exists to some extent, but not to the .7c to the dollar ratio that's thrown around. When you account for the fact that women tend to start working later, retire earlier, take more time off, are less likely to work overtime, and choose to work in lower-paying fields, the gap is more like .96-96 cents on the dollar (at least in western countries), which isn't statistically significant.
As far universities being "democratic indoctrination camps", I agree that's pretty hyperbolic, but there's a lot of proof that universities in general are more left leaning than right.