Economically: Christianity
I believe Christianity to be both economically and socially liberal. The Southern Baptist Convention doesn't speak for every other sect and denomination.
Yes. There are plenty of homosexual Christians, for instance. I thought the religion was about forgiveness and loving the sinner, hating the sin, but certain extremist denominations that also happen to be very outspoken tend to warp the general public's opinion of Christianity. A lot of Christians detest what extremist Christians say. And likewise, just because a lot of outspoken atheists are liberals doesn't mean that atheism is entirely a tolerant and liberal religion.