I don't care about having a gay character at all.
Ok.
However, if they make it a point to shove his sexual orientation down our throats over and over again
This is awfully close to what people say when they expect gay people to only be gay in private so that the world doesn't see it.
You know, what does "shoving it down out throats" even mean.
Let's take TNG for example: Every single one of the main cast was shown to be heterosexual at some point. So I don't think it's unreasonable to treat a homosexual character in a new show similarly. Where they go from there, is pretty open.
I struggle to think of a TNG character whose sexuality was rarely affirmed. They all had various crushes and relationships at some point. I suppose the one who's had the least of that was Beverly, so if the sexuality of the new gay character were as irrelevant as Beverly's, he could still have relationships and an on-going will-they-wont-they with the captain of the ship? And this wouldn't be "shoving it down out throats" because it'd treat a gay character's sexual life exactly the same way as a heterosexual's sexual life was treated.
He could also be the Will Riker of the ship and have a gay romance in basically 50% of all episodes and this would still not be "shoving it down our throats" because this is exactly how a heterosexual character was shown. And somehow even with all his affairs Riker managed to also have some other aspects to his personality, apart from his sexuality. So it's not like the whole character was only about sex.
They could also have him be married with kids like O'Brien on DS9 and have him argue with his husband all the time like O'Brien did with Keiko. It'd take a lot of screen time but this still isn't "shoving it down our throats".
Whether the new gay character lives his sexuality in a Riker or a Beverly way... I think we can be reasonably sure that the character will not ONLY be about sex. Yet, of course, if he's really a Riker kind of guy we'll see a lot of sexual content on screen, because he's like Riker, not because he's gay.