Erm. You misled us a bit there, you don't have a boyfriend. On that note, I'd say your family was more important if it was a choice between them - but why should it be? You're ok with it, he's ok with it, your cousin would be ok with it, why should your families get involved? They can't force those two to like each other any more or less than they do. So it's nowt to do with 'em.
if it were me, i'd keep my friendship with both of them and wait for the cousin to marry someone else
but you probably don't want to wait that long
so go with your head
I fail to see where the problem is... are your families like the Montagues and Capulets of Yorkshire or something? Really, what are they gonna do, disown you?
Personally the only problem I foresee is that if you do go out and it turns nasty, that might be a problem for your cousin.