Translation: they want to have freedom to discriminate people. That's just not very nice.
I support gay marriage, but I also support this couple's decision. To support otherwise is supporting the removal of individual freedoms.
The stance that "a private group has every right to refuse service for any reason." is the same thing that they said in the South with Jim Crow laws and racial covenants. So how can I say that what the couple is doing is within their rights but at the same time say that Jim Crow laws were not right? I can't quite square that circle.