"can this song be saved?"
Like a lot of things, poking fun at your own group is considered a sign of a lively sense of humour, but poking fun at another group is often considered bad manners. Chris Rock can do a great stand-up routine about upwardly-mobile blacks, but I don't know that a white guy could get away with it. Maybe it's illogical, but hell, we're human, right? we're allowed to be illogical.
And I think the song wasn't really that funny in the first place - maybe if it had been a bit funnier, there'd be no objections. The "Inner Bitch" one I did like though - I know a few women who'd enjoy singing that one.
PS. Happy to cry at weddings, and I don't feel the need to see lousy Tarantino films anyway. And my bumper stickers say "Go hang-gliding" on the left and "Give blood" on the right... ;-)