Generally speaking, yes - the Prince's sensibilities are actually weirdly heteronormative for a fae, which is actually a notable trait. However, if the person is capable of pulling off the look and requests alternate clothing choices, the servants will probably acquiesce. It's more important that you look presentable.

So I guess the status on wearing non-standard fashion choices is "ultimately accepted but somewhat frowned upon." The Prince will roll his eyes, but that's about it. Though if your character can easily "pass" as either of the gender binary, he probably won't even notice.