I would suggest that the then Corporate Cr@p network didn't like the additional competition.
Back when Art Bell was entertaining, one of his AF hitch stories was being stationed in TX. He and another guy were running some sort of broadcast as a hobby/passion, and when their "station" started appearing in the local Arbitron logs, they were ordered to close it down on the complaints of the local radio stations.
As for the church aspect, there was some legal hole that would allow challenges to NPR frequency assignments which a number of "religious" organizations glommed onto during a re-licensing period. That may have been when she was a NY senator, though.
As for this unlicensed FM station, perhaps they should follow the example of another former operator of an unlicensed FM station (a la "Radio Caroline", as well as a number of other earlier youthful pirate endeavors), Allan Weiner, and go legit?
At the time Hillary was making a fuss about LPFM, she was first lady, and the animus towards LPFM was clearly aimed at church affiliated stations. She *HATED* Rush Limbaugh with a purple passion, and given time and power enough, would have had him taken off the air, arrested, and disemboweled.