"Survive" has a strong meaning.
I hope you'll find a solution that doesn't involve having to survive, but simply live your life as a teenager.
I am sorry but I haven't faced such a complicated situation, so my advice might not be the best. However, I can tell you about my experience having to deal with a dogmatic religious family member.
These rules and dogma didn't suit well for me and my gf. Going to church, not being able to show public affection, this was becoming really annoying. When came the time to move to university, we did it mainly for our studies but then, we realized that this toxic person finally had little impact on our lives. We managed to meet interesting people and it helped us to realize that what we were living in these abusive environments was not normal. Even if you know it, part of your brain is still weirdly wired, especially if you have been raised this way. That was the part where we had the most disgust for religion and our hometown. This is a normal part of the process I guess.
Now, it's been 5 years since we graduated and I can finally say that we are not under this toxic influence. We even managed to make peace with this situation and are planning to move back to our hometown to build a house.
What I want to say is: whatever happens it will take time. For me, 16-18 was denial, 18-24 was going full SJW and by the time i hit 25 I started to make peace with the situation and started to have a more nuanced opinion on this situation. Even if we are not on speaking terms, I feel sad for these people. They have to be terribly sad or frightened to act like this. It must be awful not to be able to think by yourself and rely on a book to tell you the right from the wrong with constant fear to endup in hell.
You do not seem to be in denial so that's already a good step. But moving away was the key that allowed us to clear our mind without toxic thoughts and make peace with this situation. it's like going in a shell to properly heal.
So my advice is: do not make any harsh decision, accept it will take time and make sure that you can move away without sacrificing your education so that you can maximize your chances for independence.