Try and ask her the real reason why she might be reluctant. “Because they’re muslim” is not a really strong argument; “because they are fundamentalist and they might extrange me as daughter or prevent me fron leaving the house if they found out” is a very practical explaination on this compromise she decided to take.
Families are complicated and sometimes shitty, but it’s her family and navigating around you and them could be difficult (she might love her parents and want to maintain a relationship with them, or she hates them but relies on their financial support, both options are valid)
/swapfile joined the chat