Should I refuse to let my unvaccinated cousins around my future children
Why do you think vaccination is so important?
During my last trip to a farm, I got sick due to a disease that was transferred by a pig.
It's completely understandable given your first hand experience with disease transmission that you'd be uncomfortable letting unvaccinated people around your kids.  A parent's number one priority should be to protect the health of their children.  I think you need to talk to these cousins of yours about considering getting vaccinated.
I don't want to discuss it with them. They can think for themselves.
I'm sure they can think for themselves, but if you think they should be vaccinated you should make sure they have proper information about vaccination. A lot of people just haven't received good guidance on the importance of vaccines. They'll be much more likely to get them if they understand them.