Many Log Cabin Republicans espouse a small-government conservative view. They are arguably more conservative than those who advocate government intervention into people's personal lives. The same could not be said for those other groups if they existed.
Ah the myth of the "fiscal conservative". We've heard it before. Guess what? They don't exist. Like Olympia Snow and Lincoln Chafee and Arnold Schwarzenegger these so called Libertarian-leaning "fiscal conservatives" always, without exception in my experience, wind up showing their colors as nothing more than plain old liberals.
I know Log Cabin Republicans personally. I've seen them campaign against fiscal conservatives like John Doolittle and former California Assembly Speaker Curt Pringle, in favor of their liberal Democrat opponents. I worked with one who placed a Clinton bumper sticker on his car and in his office window in 1992.
They are liberals. Period.