I doubt his sexuality was even given a second thought. He was there to push buttons and spout exposition. Takei wasn't given all that much to work with, frankly. He was used for some reaction shots once or twice,. That's about as deep as it got. I'm not even sure how you play gay or straight without a relationship in the story.
Some people are mixing up the following concepts:
1. Is there enough "onscreen" evidence to definitively prove Sulu was gay, straight, etc.?
4. Was the original Sulu straight, based on the totality of the evidence in front of us?
From a purely logical standpoint, old Sulu is straight and new Sulu is gay.
I have to agree with @Nerys Myk. I don't recall anything much in TOS or the movies that added much to Sulu's character development, let alone his sexually. Certainly not anything that is definitive one way or the other -- gay or straight.
The problem with accepting "old Sulu" being straight and "new Sulu" being gay is that it opens up the can of worms about why a person is gay in the first place. If one Sulu definitely is and one definitely isn't, then that can be used to say being gay is a lifestyle choice. That's a dangerous place to go. Though it's not conclusive, science tends to accept that being gay is "nature over nurture" and that it is likely physiological things (genes, heredity) which determine whether or not a person is gay.
So, if "new Sulu" is gay then by extrapolation, if "old Sulu" is exactly the same person, then it's very likely he's gay, too. Of course, that doesn't speak to either's sexual proclivities or behavior as a gay man. Those can be different.