I think you may not get a ton of replies. I didn’t reply at first because I don’t have an inner knowledge of the schools you are asking about. I would say that BS is slightly more conservative than a day school in a very liberal area would be. If you live in a very conservative area then BS is going to be a shock of leftists. I’d say most of the girls are fairly liberal and many of the boys want to think of themselves as “middle of the road” but have somewhat ridiculous arguments to that effect. The good thing about BS is that conversation and above board argument (oh discussion) is encouraged. There are certainly schools where there are many more say Trump supporters (none that you mentioned) and schools that have pride flags and BLM signs on every door (also none that you mentioned).
If your child can speak logically about their views and can listen they will be JUST FINE. It’s the kids who don’t listen and refuse to learn that are going to have trouble.