I agree, this bothered me about CJ, too. Just... Note that even at that point, there are already at least two homosexual characters in the story (albeit, they're both girls, and I suppose it'd be more accurate to say one of them is bisexual; the other will inevitably end up being… well, forced into bisexuality, in a way). Later on, there's at least one explicitly homosexual male and one bisexual male, one of which is… I can't really say without spoiling things, fuck. And it doesn't seem like there's any way to spoiler tag text on this site.
It concerned me, too, but as the story progresses you'll come to realize that CJ's attitude towards homosexuality isn't as bigoted as if might have seemed early on. Remember that he's still pretty much a kid, he's got a lot of growing up to do. CJ may seem to be the protagonist, but I'm my opinion, that's not really true. Each of the girls in his polycule are just as much the protagonist as CJ is, if not more so. You spend more time getting to know each of them from their perspective than you do getting to know CJ from his. In fact, you almost never see things from CJ's perspective beyond the prologue.
Let's be real, here: CJ's entire ‘look’ is incredibly metrosexual. Seriously, he practically screams “I'm a closeted bisexual guy!” I think that if Jamie had turned out to actually have a dick, CJ would've made it work. As in, they'd eventually have fucked.
See, CJ is terrified of being emotionally vulnerable around others, even those he's intimately connected to, just like most men are. It's the same shitty reality that the majority of men in the present day face. There's a lovely phrase for it: toxic masculinity.
He feels as if he has to always be the “man,” always has to support those he cares about, and that if he ever allowed them to support him instead, he'd somehow be rendered incapable of continuing to provide that support to others. It's genuinely really fuckin' sad.
That said, he grows up a lot throughout the story. Early on, you'd be right that he gives off some very distinctly homophobic vibes, but later, not so much; though, doing get me wrong, they're still there (it's not as if he's dealt with them, after all), they're just not being actively expressed.
I've just reached around chapter 35 and he's still not confronted this part of himself, and I'm not sure he even will within the next X chapters—before I reach the end of the content that's currently out—but I would be very, very surprised if this wasn't addressed by the end of the series. Several characters struggle with their sexuality in different ways, one of which is explicitly a struggle with homosexuality, and the writers always deal with such topics with maturity and respect. For example, the relationship dynamic that they ask have is far less a “harem” and far more a polyamarous polycule.
Remember: a character's beliefs and actions are not the same as the author's beliefs and actions. Without conflict, one can't grow. You can both dislike CJ's homophobic behaviors and still love the story and characters. These are not mutually exclusive things, after all.