Yes, technically the church is simply collecting the tax, the buyer is paying it. However the church does not pay property tax, income tax, or any other tax really. I think from my distant past years in retail (high school) the church doesn't pay sales tax on their purchases of supplies either. A business owner must pay all of these. And in NJ where the story is taking place, that extra burden is not small.
Basically the market is distorted when some participants have a large tax burden but competitors do not.
Yes, those are good points.