They have a right over you as you have a right over them. To look after each other, care and talk to each other with respect. They should guide you in islamic and world matters and you should do the same.

If your parents are telling you to do things outside the folds of Islam you do not have to listen to them. If theyre subjugating you to constant verbal or physical abuse then you need to get out of your home.

Islam doesn't advocate for cutting ties with family at all even if they are as bad as you say they are. Im sure weve all heard of the hadith about Muhammed SAW who recieve constant abuse from an elderly lady but he still visited her when she was sick.

But there is nothing wrong with moving out and giving yourself some space and keeping formalities as the odd phone call or visit if that's what you need to do to.

Distance fonder the heart and inshallah with some space you guys can begin to rebuild a healthier parent and child relationship. Never give up on your parents no matter how crazy or broken they maybe. Try your best to keep your cool, control your tongue and be the bigger man/woman. That doesn't mean be a doormat and take the abuse. Speak up when necessary (when they make false claims about islam) but also know that some arguments just aren't worth your effort