Is haku gay

I feel like Haku is legitimately a girl but had the line saying she wasn't as like a joke to throw people off. or they went in fully intending Haku to be a boy but trapped him up.

I don't think that Haku was acctually gay. Unless my memory is just completely off there are several societies that considered a select few boys who wore girls (or girl-like) clothing to be a sign of intense purity.