@wandeljw,
When I was younger and more idealistic, I, too, placed a flyer or two beneath other people's windshield wipers. I assure you, it's quite possible to do that without asking anyone's permission. I don't know if this is legal, but I do know it's easy and usually hazzle-free. Besides, any legal problem would be the activists', not the church's.
But I don't think your claim holds even on its own terms. If the activists asked the Church for permission and got it, I don't know that's a problem unless the Church denied similar permits to Democratic activists with similar flyers. Do you know that it did?