IDK if this is true or not, but I can say as a Catholic this is NOT the case in my small neck of the woods. The number of families with growing numbers does not seemed to have slowed.
Being part of the parish's Stewardship Committee, I get to see a list of all the members of the 2 churches and their family members. It has risen by ~7% consistently for the last 5 years (since I started managing the data)
The schools are growing at nearly the same rate as well.
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