Id argue it isn't even homophobia, he just doesn't like dudes <3
Ehhh the constant use of fag, talking about how they shouldnt think about it since its illegal. He's definitely not the worst type by any means, he thinks his friend is gay yet he's still very nice and supportive, even loving to them. It's just a weird amount of implicit homophobia, which is a real thing even among generally good people because of social conditioning, the thing that makes it weird is that CJ sorta seems immune to social conditioning in most other ways. Also, he looks like the queerest dude alive so there is a bit of projecting there. Again, its not terrible, just a bit unnecessary in my opinion. It could even have been a really fun dynamic for him to think Jamie is gay, and be overly supportive about it, while everyone else knows the truth. I'd argue you'd get better jokes out of that than just the constant "don't be a fag".
Only going into it this deep because the game is great tho, most other avns never touch the subject or are frequently way worse about it. The only one in my memory that did an A+ job on it is realm invader, highly recommend it!