This love interest has
way too little respect for consent. And in that context his smarmy-ness is the antithesis of attractive. Ew.
@Thrembs:
To be fair, to my (imperfect) recollection the current science says even first-cousins having kids is probably usually fine so long as it's not a constant thing you keep doing over generations (the normal example I would have used here is European royalty, though I can see how being part of any small pocket of a in-marrying, frequently-ostracized, matrilineal-descent-based group in the middle ages could have pretty much the same devastating effect. Alas.) This in contrast to siblings, which are always a no-good very-bad idea.
Of course here we deal with gay couples who couldn't have kids anyway—but holding gay pairings to a different standard for just that reason would seem rather unpalatable as double-standards go.
None of which has anything to do with ick or squick, of course. Nor non-health related moral issues (which are to
some extent context-dependent but do, I think, show up here—namely the fact that the protagonist at his cousin's house because family is presumed
safe and (by the same token) handling his cousin's goddamn
consent problems here would be an incredibly fraught issue compared to something you can walk away from. Nowhere near as bad on that front as siblings could be, mind.)