The house I lived in from the age of 3 until I moved out on my own was directly across the parking lot for a fairly large Catholic church and school. This is in New Orleans, where a sizeable portion of the population is Catholic, but my parents were Baptist.
It usually wasn't a problem; the church had adequate parking for their regular school and Masses. But twice a year the school had a fair, when the parking lot would be filled with amusement park rides, and the worshippers and school attendees would have to park on the street. Also, because of the location of the church and school buildings, the noise tended to be focused right on our house. But it wasn't very often, and we put up with it. After all, we knew the church was there when we moved in.
The biggest problem was Easter and Christmas, the two masses which are the only two days many people ever bother going to church. For years we would have great trouble getting our car out to go to our own church. One year one of the churchgoers parked between our driveway and our neighbor's, with the rear bumper of his car blocking our driveway and the front bumper blocking the neighbor. It was quite impossible for us to get our own car out past it.
My Dad, who is about the least confrontational person you can imagine, walked across the street and into the church just as Easter Mass was starting, and loudly announced that if the cars blocking our driveway were not moved immediately, he would be calling the police.
It didn't happen again for many years

Also, when I was about ten years old the church decided it would be classy to install bells that chimed on the hour. Except they weren't quite classy enough to get a real carillon; it was a tape recording of bells. Again, the sound was focused on our house. And they ran 24/7. That time it took actually calling the police to get them to stop playing the tape at night.
It sounds like this situation started similarly, except that instead of the church and neighborhood meeting half-way as my parents and the church across the street usually managed, each side has gotten pissy about their "rights" and climbed up on a high horse about it. It's not about religion at all; it's about being bad neighbors all around.
It may be legal to have cars parked all up and down the street in a residential neighborhood because of your activities, and in some places nobody would care, but if it's causing a problem and there are complaints then you need to move the activity or come up with a solution. And if you're the neighbors you need to accept that a certain amount of this is acceptable; as long as you can get out of your own driveway, find parking for your own car, emergency vehicles can get through, and it only happens at predictable and relatively infrequent times, then you should put up with it. After all, you might want to have a birthday party or wedding reception one day.
Unfortunately it only takes one side being unreasonable and it's hi-ho, hi-ho, off to court we go. And it sounds to me that in this case both sides are being unreasonable.