I don't know how much of a focus she's putting on religion, but if it's a decent amount, I'd suggest looking up all the places that mention being trans in a bad light. If the religion is Christianity, it's 1. Then read the rest of the same chapter with them, so they can see that the other verses in the same story apply to them too. It's surprising that a religious discussion would ensue if she's pro LGB though. They're spoken of much more harshly in the bible.
Parents blaming themselves is normal too. It took my mother about 2 weeks to come around to talking to me and she cried the whole time. It took another few months to be okay with it all.