The culture in Athens, GA does not equal the culture in the rest of Georgia. Although the majority of students there are technically from Georgia, many are from metro Atlanta and have family backgrounds and heritages that span the globe. Atlanta has grown from two million to six million in the past couple of decades, so the students originating there can have families that came to Georgia from anywhere. Atlanta is also well-known for its support of gays and blacks – two liberal agendas – and the students hailing from there may be more liberal than you expect from Georgia students. UGA of course also attracts students from other states and countries who have a variety of beliefs and political values.
I suggest you visit Athens and see what you think. My personal impression, having been there many times, is that it certainly has its share of alternative types and plenty of liberals. With the strong music scene, there are many creative performers who call Athens home. Is it still part of the Bible belt? Yes. Will you still meet some students who grew up attending church every weekend and who cherish conservative values (no matter whether they party the night before at the frat house or not)? Yes. But you will meet all kinds of students, and professors tend to be liberal everywhere.