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It depends for sure. However most households have a diversity of friends and the kids do have to go in group outings. Besides, depending on school district your claim might not be accurate (ie you may attend a school full of rich brats, you may attend a school full of ne’er do wells, or a school where everyone is on the lunch program) neither broadens horizons).

Religion might be a problem with strictly religious parents, but I don’t see the damage being worse than that done by school systems. I experienced way too many friends who didn’t fit in and dropped out and other kids who believed in the system and believed things their teachers told them.