Agree with others, this advice is not only inadequate but actively dangerous. The parents are homophobic, and they haven't really reached the tolerance / acceptance level though they're sort of aiming in that direction. The LW is not "privileged" because her life doesn't look like the worst melodrama image of coming out to violently homophobic parents. I strongly suspect these parents are capable of deliberately wrecking their daughter's life if she doesn't conform, even assuming they would stop short of direct physical violence. I'm not sure I really believe that LW has an otherwise excellent relationship with them; children love their parents, it's a thing, even if the parents are outright abusive. The situation described may not be extreme but it's still dangerous and provoking arguments with her parents in order to stand firm on being your authentic self is going to backfire badly.

Also this letter is from a child. She needs more than just advice and resources, she needs to know how to access someone with the authority to protect her if she needs it.