When the author doesnt believe trans people are real, then to the author all trans people are simply "cross dressers".
Let's step back a bit from assuming anything about the authors beliefs shall we?
The thing is, these characters tend to "cross dress" all the time, which falls out of the realm of what someone cis would do.
This is a fictional story. Artistic liberties and all that.
Like why is his despair of potentially being gay a funny situation?
Ok, I'll take a crack at this. In a perfect world, worrying about your sexuality is utterly pointless, because nobody would judge you for it. One of the great things about fiction is that you can create a perfect/near perfect world, and use it to explore ideas that you like, without having to drag real world social issues into it. This is especially important being that this is a comedy and, nothing ruins a light-hearted tone like reminding the reader that the world is a shithole full of horrible people.
That being said, this is a world where the norm is that guys have no problem crossdressing at all. With that in mind, it is comical for the MC to be worried about being seen as gay, when nobody else gives a shit. Juxtaposition is one of the foundations of comedy, and in order to turn something serious into something funny, you have to juxtapose it with something that brings out the absurdity in it. That is what's happening here.
MC is worried about being seen as being gay. That's sad. How do we make it funny? We make it take place in a world where guys wear dresses without giving a shit about how it makes them look. Now the MCs worries are completely unfounded, and we can instead highlight the comical nature of the whole situation.