Georgetown is a Jesuit university. It used to be funded by the catholic church, but the church actually revoked its funding because it's policies were too liberal; that has always been the split between the catholic church and the jesuits, since they were the intellectual thinkers of the church. I was a student there and I know that there are many Jesuits and professors there that are supportive of LGBT students and their causes. I can't attest to the work environment, but I have many friends who were out while at school there (I was not out) and had a positive experience.
If you are questioning how accepting they are, simply ask them. I think it's an important question for LGBT to ask in an interview. And, frankly, by bringing up the topic it lets them know you're gay so they know who you are when they hire you.
I do believe that Georgetown was against Obama's mandate for insurers to provide free birth control to women. I know that's a separate topic, but it goes to show that the university does have conservative values.