The Eurodam seems to be this group's go-to ship. We were on a Caribbean cruise on the Eurodam about 14 years ago and their presence was very noticeable. Many venues were not accessible to the other guests.
If my memory serves me correctly, it was not the friendliest group of people and as someone mentioned, they didn't mix with the other passengers. We made sure we were not on one of their cruises after that. It's been many years since then, so I hope it's different for you.