Interesting posts to be sure. I say since your cousin and his 'other' were good enough to come to your wedding ( as you requested) then you now should return the favor.
If you wanted to make a stand against his 'beliefs' you should've started by inviting him to your wedding WITHOUT his 'other'. So I can't see how you can now say they're not good enough to 'accept'.
OTOH the chances of this marriage lasting too long are practically nil, but your cousin will always be your cousin and could probably benefit from your future counsel when his 'failed' marriage occurs.
they have been together for at least 15 years already......maybe 20 years