I’m assuming you did this, but make sure you mention to her Mom the details of her disruptions (sex, drinking). If I had a 13 year old, I would definitely want to know and would be very concerned. If Mom is still not alarmed, she might be aware of her (hopefully attention-seeking) outbursts and hopes church will help, or she’s just not a very active parent. It’s always hard to tell what the situation is like at home.
If you’re comfortable with it, I would pull her out of a full class for a discussion with you. If there’s anyone that she listens to, it might be a good idea to have them present too. Manners are universal. Explain that it makes no difference if she chooses to identify as atheist, Jewish, Buddhist, or Catholic, manners are required, and that includes not interrupting when others speak and respecting the teacher. Rude behavior is just rude, and her beliefs don’t excuse her for that.
Now, the second part about religion is more tricky. I would ask her why she continues to attend class if she despises it so much? Is someone making her or is she electing to? In either case, what are her specific objections? Make her explain her beliefs, not just say she “hates church/God/etc.” Why does she? Hopefully these questions clear up whether she’s just looking for attention or she has actual problems with what’s being taught. If she has real issues, let her vent and explain where she’s coming from. Who knows what her past is or what experiences she may have had that could lead to this sentiment, but her doubts certainly deserve to be heard by someone who cares about her (and it seems like you do!). I think that with all these cards on the table, you could have a more constructive conversation with her about her beliefs and actions in class. It’s always easier to talk to someone (including 13 year olds) when you know where they’re coming from.
If she continues to disrupt class by proclaiming her hate for church/God, make her explain why in front of the class in a debate style. If she wants to announce her beliefs then she’s going to have to defend them. Force her to go beyond “It’s stupid” and give you real information. It will get her thinking about what she really believes and will probably bring up a lot of great questions/learning points for the class. I don’t know how you personally feel about religion, but I believe that a little debate can start a really great discussion. It’s important (again, in my personal opinion) that both she and the class learn to respect the beliefs of others and be able to discuss it in a manner that is not offensive to either party.
Finally, props to you for wanting to help her! As they say, it takes a village to raise a child, and I hope you can have a positive influence in her life.