Of course things can be taken too far or into the extreme.
I'll be consistently telling her why she shouldn't have such an account, but that's just what a father would always do and can only do if your daughter is an adult.
Now, if my wife or girlfriend was in this situation, I'm breaking up with her or divorcing her ASAP. If she doesn't remove or delete her account after I've told her I don't like it, I'm leaving or divorcing immediately.