I find the comment saying that she'd still 'have' to kiss a girl if she were the princess slightly homophobic. What, so that's assumed to be the most disgusting thing ever?
I agree with posters saying that she may well not get a part, or a big part, if she turns this down, and she needs to accept that. In a girls' school, she also needs to acknowledge that most people who wanted a part, would have been pleased to get the part she has.
But, I think you need to work out with her why she is so upset. If it's that she would have preferred a 'girly' role and feels her nose is out of joint, I'd have little sympathy. But if it's that she feels someone is saying she's masculine/tomboyish and that actually upsets her sense of self, then she does deserve some sympathy. At her age, it can feel quite upsetting if someone says 'oh, so-and-so looks like a man, she'll do it'.
Equally, if she's already being teased about something, she might feel sensitive. Children can be cruel. It could be someone has said she is a tomboy, or she's a lesbian, and those things have upset her. I remember shying away from acting at school, for precisely those reasons - I was worried someone in my girls' school would tease me.