Where I live Catholic schools are closing their doors left and right. Many"Catholic" families send their kids to the parish school and identify themselves as parishioners in order to get the discount (much bigger than$400 here though, so maybe that's part of our problem) yet I've never seen many of these families at Mass, ever. In fact, this week is Catholic schools week and we went to the Catholic schoolnMass and i was wondering where are these kids that go to this school. Where I live, the parish and the diocese pays a substantial subsidy to the schools and tution rarely covers the costs of educating the child (we no longer have nuns teaching for free). Where I live, we are all suffering during this economic downturn, wages are down and costs are up. Parish donations are down and essentially a private school education is being had by many families on the backs of true parishioners ( we homeschool so perhaps I am a bit begrudging, my parish offers NO homeschool support whatsoever). The way I see it is your parish is committed to having a school not just for this generation but for all generations. If we had had a bit more of that foresight here we might not have to close all of our schools within the next ten years.
As for background checks, um, given the scandal that has plagued the Church around the world, they have become necessary. So having parents reject the background check truly makes no sense to me. In this sense and for other liability reasons, it makes sense to me that only enrolled children and approved volunteers are on the grounds.
Yes, that means that there are a lot of parents around, but it helps reduce the temptation to get a private school education for essentially less than the cost of daycare ( which sadly tends to be the norm around here), with parents still complaining about the costs. Gone are the days when you were baptized, confirmed, married in the same church, where your lifetime contributions to the parish far exceeded the discount on the tuition rate you paid for school. Where parish membership didn't decline steadily year after year because parishioners are picking and choosing which rules to follow. Eta- where I live most private schools, even religious ones other than Catholic, run about 8,000-15,000/year, so Catholic school at $3500 is a bargain and many people take advantage of that without a second thought, "Catholics" and noncatholics alike.
It is surprising though that as a Catholic school there aren't other families with childcare issues ( though considering the avg # of kids per family in my diocese is probably 2 or less perhaps not so much).
I'd pay the fee and be done with it. Let whomever offers the slightest indication that you are somehow "less than" come over and watch your kids while you go and volunteer

As for the official tithing, well many synagogues ask members to pay annual dues and for Mormons tithing is a pretty standard thing too I believe, so it doesn't strike me as so horrific if another place of worship strongly encourages the same.
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