Non-destructive assaults are so much fun.
We should just lob pigs at it for a while. Woohoo!
(ahem) In all seriousness, according to the Gentlemen's Laws Of Civilized Warfare, hiding in a religious building, shooting from a religious building, and using a religious building for a military base all invalidate the "holiness" of that religious building. If somebody parks their tank in the front courtyard of a mosque, and my helo-fired-rocket does damage to the mosque collateral to destroying the tank, that's considered acceptable. If I have to invade a mosque to suppress fire from within, that's considered technically acceptable.
OTOH, the Arab world would be in an uproar. Al Jazeera would claim that the evil blood-thirsty infidels violated the holiest mosque of the holy (may his name be blessed) Muhammed and that our blood should run in the streets. Then the mush-heads of the general American populous would quietly believe these things, as many of our news outlets seem to mostly paraphrase Al Jazeera, and would be upset about what we had done.
So it's a lose lose situation. You leave the rebels there, they cause nasty problems. You go in and get them, your own people rebel against you. Bummer.
Dan