My daughter definitely felt that way at Smith at her overnight, and knew it wasn’t the school for her. She was grilled about how she identified and asked a lot of personal questions she wasn’t prepared to answer.
I think at some schools it would be an issue (including BYU) like Liberty, Ave Maria, Bob Jones, and many of the small LACs in the south. At many of the LACs, it won’t be a problem or even questioned.
I was born and raised in the South, and the only homophobic comment I’ve ever received was in Santa Monica when a fellow took offense to my boyfriend and I holding hands in a coffee shop. There’s still pockets of bigotry everywhere, unfortunately.
As others have said, most colleges are pretty queer-friendly these days. Some colleges have much smaller and more incestuous dating pools than others, however – something to consider when looking into colleges that are particularly small and/or rural. Due to the lopsided gender ratios at most LACs, the dating pools are usually better for queer women than men, though.
I think, if my 25 yr old daughter and her friends are typical, this generation honestly doesn’t care what your sexuality is. They are very accepting of whatever you want to do. I do notice a lot of young people chose to come out as freshman so they can start their new life at college with their new identity.
I didn’t see it mentioned yet in the comments, but the website https://pflag.org/ can be a great resource. It is for parents of LGBTQ and it was a terrific resource for me when my son came out at the age of 13. They have really great resources for you as a parent if you are struggling with your own emotions and fears. 
I wish you and your family nothing but the best.
The non-profit Campus Pride Index is a big help, and the fact that it exists is reassurance in itself: http://www.campusprideindex.org/.
The good news is that, at the most liberal schools (even small ones), being gay will be almost a non-issue in this gender-and-orientation-plural generation, and she’ll have plenty of company among those similarly able to be out now; and at larger schools - as long as they’re not conservative - she’ll likely have even more company, especially since such schools are often in more densely-populated locations with lots of diversity and resources and sophistication. The LGBTQ community, is, like other sub-communities, a great way to find friends, and tends to be particularly welcoming - sensitive to the needs for outreach and acceptance. Most schools now have gender-neutral housing options, and may work out roommates on a case by case basis for people with non-conforming gender identities or orientations - its now well-worn ground.
But our polarized society may make it harder for her to be at conservative schools, especially those with a religious focus - often (but not exclusively, and not universally) in the South. That should be a real consideration in her college choice.
If you haven’t seen it already, I recommend the movie “The Kids are All Right.” It will remind you that challenges around bigotry, reproduction, relationships, and raising kids are things everyone may experience in some degree, and at times. Being gay neither fully creates, nor fully saves one from, any of them. It’s just one part of some people’s lives – one way to be.
Houston had a very popular gay mayor for a decade. Times have changed.
You are not alone. Not even close. If your D is happy you should be, too, although it may take a little while to get there. Welcome to the 21st century, I guess. To tell you the truth I was shocked at how OK I was with it. You don’t need to be worried for her.
My kids are straight but I thought I should mention that at my DD rah rah big public university there were girls in her sorority that were gay and bi. This was not an issue at all for anyone. Your D may have no interest in Greek life but one of the gay girls mom had told me that her fear had been that this wouldn’t be an option for her daughter and was pleased that it was. My D said several frats also had gay guys. This was a liberal college in the North so may not be the case everywhere.