You have received good information about several schools in the South. If your daughter is seeking a more liberal campus, then look to the cities. Cities like Nashville is very blue with democratic majorities and even liberals. Southerners are church attenders and often Baptist or evangelical or Church of Christ. It is necessary to distinguish Christian schools like Belmont (great in music) Collete from schools like Vanderbilt that are excellent academically and socially. Nashville is wonderful! College towns are probably a better match than colleges in smaller communities.
Nashville is very different from when I was a,child. My family was democratic with a liberal bent. Race and religion were core socially. My grandparents were wonderful about getting Catholic granddaughters to Mass, but expected us to toe the mark such as dressing for dinner and saying yes mam or yes sir when speaking with adults. There are traditional black behavior that still happens to a small degree with some AA teens such as calling me Miss Susie. Neighborhoods, shopping malls and schools are about as integrated as elsewhere. A big difference I see in various areas is architecture. Nashville is growing fast with lots of buildings that look like made of Legos