Unless, of course, it were proven that the mosque's founders, funders, etc. had direct ties to terrorist organizations. I'm not altogether sure, but it seems to me that, if that were the case (and I am not alleging that it is the case, I am only posting a hypothetical), then perhaps that might open up legal means for stopping construction. (?) Short of that, it seems fairly clear-cut to me that they have the constitutional right to build.
