Simple. They spend as much or more on the program than the gov't funds. Its not rocket science. In fact, all gov't funding as similar strings attached and they are monitored.
Using your test, how can we be sure the money for roads are not ending up in the pocket of a Muslim who will spend it on preaching Islam?
You create a straw dog designed to appeal to the fear of bigots rather than to beat instead of a substantive argument against.
That argument is absurd. First of all, the organization is getting money because it is religious; Islam qualifies. A road construction company run by Islamic people doesn't qualify as a non-religious, non-charity. Second, charity is much harder to track than roadwork. Finally, you say I'm appealing to bigotry when we've illustrated time and time again on this forum that very few Islamic organizations are free from anti-semitism and anti-Americanism. I think you're simply defending the party when the party has gone out of bounds with its president leading the way.