LGBTQ+ people are human too—they can have flaws, desires, wants, etc. This also applies to their potential to take on antagonistic positions. It isn't inherently racist or sexist or homophobic to have a person of any race, sex, or sexuality be a villain, because those traits do not define their entire being or personality. It's an aspect of them, but does not wholly define them.
In this instance, they aren't antagonists because of their sexuality, but rather because of their ambitions, which run contrary to the main character's interests. If you swapped the MC's cousin to be female, you'd get a fairly common story. I don't see how changing the villains to be homosexual makes this homophobic; it's just a cliche plot. Without more information, or more emphasis on that detail in particular (of which there hasn't been that much tbh, and we've only had 6 chapters) I would not rush to conclusions on the author's personal opinions.