I think there's the immediate reaction of "No, fucking your cousins is weird, I don't like it," and then right after that, you go "...but, now that I think about it, I don't really know why I think that this is bad. Hm." Which is a good impulse to have! It's good to be inspecting your own beliefs and overcoming reactionary disgust! It's also entirely possible to then go "...no, actually, I do think this is morally bad even if it's not necessarily always genetically bad; this isn't just me being ruled by harmful cultural norms or something like that."

Here's a question to "calibrate" your moral compass in this situation: Is fucking your stepsister or stepbrother a bad thing? I personally think that it's pretty taboo, despite there being no genetic relation there (within reason). Why is it taboo despite the lack of blood relation? The answer to that question should help inform the answer to the cousin question.