Their answer: claim Islam isn't a religion, it's a political movement.
It's hard to decide which part of this desperate attempt to legalise bigotry is more ridiculous. It's definitely either the idea that a religion that demands a certain way of living is actually a political movement, or it's the idea that political movements aren't protected by the First Amendment in any case. You can toss a coin, pretty much.
I got this story from Glenn Greenwald's twitter feed, which he accompanied with a comment along the lines of "Look what the Republican big-wigs have wrought" (that's a paraphrase; I don't think Greenwald's the type to call someone a "big-wig". See, I think he's being unfair here, because if we look at what the Republicans are actually demanding:
DeMint said if someone is openly homosexual, they shouldn't be teaching in the classroom and he holds the same position on an unmarried woman who's sleeping with her boyfriend — she shouldn't be in the classroom.it becomes entirely clear that the last thing they want to do is stop religious movements from prescribing what the entire country can and can't allow. Remember, kids, we must make sure that Christians never lose their inalienable human right to not be taught by someone they don't like! Gays are icky! Unwed sexually active women are whores ! We must ensure our teachers are free from sin in order to conform to a religion that specifically states no-one is free of sin!
Doubtless DeMint will be denouncing these people any minute.
 Note that Jim DeMint doesn't stake out a position on batchelors who are getting laid. He's a despicable prick, but he's not totally stupid.