Actually Bryn Mawr IS a quaker school. It was founded by quakers and is still on the list of Quaker higher education schools.It is also part of the Quaker Consortium (haverford, bryn mawr, swarthmore, upenn). But this does not mean it is accepting of all beliefs (and by this i mean conservative views).
I was recently accepted and planned on enrolling at Bryn Mawr but chose another school due to financial reasons. I also have a close family member who works in the administration. I AM extremely liberal so Bryn Mawr’s political views were not an issue but rather an attraction to me. This being said, this is not the school for you if you are conservative or libertarian. I read an article not long ago about a Bryn Mawr student who asked the student body if anyone could give her a ride to a Trump rally. She received so much backlash she transferred to another college.
http://www.philly.com/philly/education/20161225_Bryn_Mawr_student_hounded_after_asking_to_share_ride_to_Trump_event.html That is the link. here is also a link referencing a student protest:
http://www.philly.com/philly/news/20161117_College_students__double_protest__Trump_and_Lower_Merion_police.html
Bryn Mawr seems to pride itself on its liberal view points and political activism is BIG on campus. I know many current students who would pretty much say most everyone is a feminist there. I know you say you don’t mind sticking up for your beliefs if challenged but it is likely that you would receive backlash and direct hostility for your beliefs and many would be unwilling to hear you out or debate you. There is very little representation for conservative viewpoints here and if Milo Yiannopoulos or Ben Shapiro ever stepped foot on campus there would be protests campus-wide (remember what happened when Milo tried to give a speach at UC Berkely? it would be like that). My family member in the administration can attest to this as well as the fact that the administration is as well fairly progressive and liberal.
This is not to say there are not conservatives on campus: http://www.brynmawr.edu/activities/studentorganizations.shtml#service
On this page you will find that there is a conservative group on campus (no contact info though-which is strange because every other club has contact info) but I would guess that they do not have a large presence on campus. You seem like you would thrive where there is a larger conservative presence on campus for you to join.
I hope this response is helpful so that you don’t go through what the girl I mentioned before went through. I know how frustrating it is when someone refuses to hear you out on political issues. I wouldn’t consider this school if you want to go somewhere where conservative viewpoints are accepted and can be debated in a civil manner. I think you would thrive at a school with similar attributes but a different political scene. There is a school out there for everyone! As much as I love Bryn Mawr, if I were conservative, I would not attend Bryn Mawr I would find somewhere with a better fit.