''Normal''??? wth
Y'know, it's exhausting being something that most people regard as strange or unusual, especially in a society like Japan where conformity is such a pivotal part of social dynamics. Wanting to "be normal" doesn't necessarily mean you want to not be gay, but normal people get to just casually express interest in the opposite sex. Romance isn't a minefield for them, people naturally assume that if they're close to someone of the opposite sex there might be some kind of attraction there, so if they confess, it's pretty unlikely to blow up their entire life, ruin their friendships and family relationships, or get them ostracized at work.
Like, here there's this girl. She thinks she's cute and cool and awesome, she's crushing hard, she joined the theater troupe just to meet her, but she has to be terrified just telling this girl that she's gay, much less that she's into her. That sucks! It's hard. The director being openly gay helps, but a lot of people are fine with the opposite sex being gay, because they feel like it doesn't involve them, so coming out as a lesbian to this girl is still really hard for her.
A lot of people in the west take gay acceptance for granted. I've run into that myself at times. And we've made great strides! But it's not a given, by any means. Every little coming out is a risk. It'd be really nice if it wasn't.
It's pretty typical to long for that kind of normality. Maybe she means she wishes she wasn't gay, or maybe she just means to wish that being gay was normal in her society, we'll have to wait. But either way, the sentiment is pretty relatable.