I don't think anyone here is saying that it does. But it was still relevant enough for at least 12 characters in this film to have heterosexual relationships. It comes up quite often.
I agree. The new film had Kirk in bed with Gaila, and Uhura and Spock sharing a private moment as well. Obviously it does matter what consenting adults are doing during their off-duty time in Star Trek.
I don't want to see Sulu made gay just because Takei is gay. Seems kind of a silly rationale. Plus, we know about Demora, although he could be bi. Since I've heard it speculated the new Chekov might be a different person than the original Chekov, as he is four years older, he might be a possibility. We know so little about him.
Otherwise, unless he/she is the main villain of the next film, there's not a lot of room for a gay character in the cast. Would gay Star Trek fans be open to the first major gay Star Trek character being a bad guy. Hard to say. Extras and red shirts aren't important enough to get backstories one way or another, so if we are to see a gay character in the next film, it has to be one of the relatively important characters.
If they ever get around to doing a new series with new characters, including a gay character in the main cast would be the best way to go.