A gay republican. It refers to Abraham Lincoln - a Republican president whose sexuality has long been debated. Abraham Lincoln was born in a log cabin. Hence, Log Cabin Republican.
Person One: Rzs must be a queeny fag.
Person Two: Really? Isn't he a republican?
Person One: Yea, a log cabin republican. Just like Larry Craig.
Person Two: So, is he also a self-hating bigot?
Person One: Honey, all log cabin republicans are.