I’m an incoming freshman, not a current student, but nevertheless I feel like I can offer a few answers (to be taken with several grains of salt):
- Yale has a thriving, though niche, conservative scene, with a host of groups and publications on campus. You can definitely find your people if you want. As for the liberal masses — my intuition is that respect begets respect. It also seems like discussions on social issues (systemic racism, anti-LGBTQ sentiment, misogyny) generate more heat than abstract economic ideology, so libertarianism shouldn't be too inflammatory.
- I'm not too sure, but Yale does have the Yale Political Union which is a cool way to supplement your poly sci coursework.
- This is really Yale's forté, relative to its peer institutions. The res colleges foster a sense of community from day one and the university's attention to undergraduate experience results in all kinds of "fun stuff," to speak eloquently, like butteries and in-house movie theaters and whatnot. Yale often ranks as the happiest of the Ivies, so the balance is perhaps better than what you'd find at many otherwise comparable places.
- I chose Yale over both of the two private schools you mentioned, and IMO Yale is sort of like the optimal combination of Harvard and Princeton. It has more of an undergraduate focus and educational emphasis than Harvard, but less of the academic rigidity that marks Princeton (as evidenced by more constrictive Gen Eds, the absence of the double major, the relative difficulty of getting into grad classes, etc). I think it strikes a good balance between intellectual attention and intellectual freedom —nurturing without limiting. Plus, for the hedonist among us, there's everything I mentioned in point 3 :)