If you’re friend tries to come out as pan, one of three things could happen: their mom would say it’s just a phase, their mom could hate them for it, or their mom could actually realize LGBTQ is not a bad thing. Most likely, they would probably say the first thing. There’s no good way to convince their mom, the best would probably be what Insomnicat said, though if that doesn’t work, you could try coming out. It would likely end in punishment and probably isn’t a great idea, but it could be your best chance, you’d have to convince her it’s not a phase though, and your friend would have to do it