Define "group" then we can have discussion.
Pedophiles?
Polygamists?
Bestialists?
Sado-masochists
Sure these are all "groups", and they've been around for centuries. Doing their thing.
Marriage has never meant anything other than man/woman.
Because someone simply WANTS something doesn't mean they are able to redefine everyone else's beliefs.
That's a two-edged sword. You just cut yourself with it.