First of all, why is everyone mentioning kids and birth defects? They're teens and it's only one generation.
OT: I personally find it pretty gross, and last time I checked this is the mainstream opinion. However, my opinion isn't what matters, it's how they feel what other people will think of them.
Do they really want to have the stigma of having had sex with their first cousin just because their horny? In love, eeeeh, I'd still ask them to reconsider. But just based on physical impulses alone? No way.The social sigma attached to this is way to heavy and I doubt it's baggage they'd be willing to carry, and I doubt they understand how big of a deal it is. As a friend I would point out what other people will think if they find out, but it will become his defining characteristic.
Does you're friend want to become "that guy who fucked his cousin"? Seriously make him consider the implications of what he's considering.
And besides, his cousin isn't the only hot person in the world.
EDIT: I see all this crap "Well if they're in love..." They aren't in love, they're two teens who want to have sex. Also to further my above point about if they can handle the social stigma, I doubt he can. You, as his best friend, are already concerned and he's trying to rationalize to you, someone he respects and trusts.
If he's rationalizing to you and you two are close, he can't handle the public eye.