Can't speak for all liberals. But my objection to the religious right hasn't ever been how they choose to live their private lives. I think their ideas about everything are a real bummer, but it's not for me to say if you want to impose that meshugas on yourself.
I do, though, strenuously object to their attempts to impose their religious notions in common areas of public life and -- now -- even to dictate how others live their private lives.
That's the difference. There's no bothsidery here.