Sorry, Dave. Not only do they not have such "a right," but to allow them to build on this site is about as inappopriate as it gets. Moreover, while the clueless think it would send a positive message to the Muslim world--that Americans are considerate of Muslims' feelings--it would, in fact, send a terrible one--that America is such a jellyfish, such a pushover, that it's only a matter of time before Islamic law will be calling the shots world-wide.
Update: From an editorial on the non-wimpy NRO site:
This dispute has been presented as a question of whether an Islamic center and mosque should be built in proximity to the scene of the worst act of Islamic terrorism — and the worst act of political violence — ever committed on U.S. soil. But at least as germane to the dispute is the question of whether these particular parties ought to be doing so. The fact that an apologist for terrorists and an associate of terrorist-allied organizations is proceeding with this provocation is indecent. We have thousands of mosques in the United States, and who knows how many Islamic cultural centers in New York City. We do not need this one, in this place, built by these people. We’re all stocked up on Hamas apologists, thanks very much.