And as they often have large families, their children have a large number of sibiling so aren't lonely, so they presume it's all good. Which just leads to entire families of socially inept homeschoolers.
Whether or not religious people retain their views is not the benefit of socialisation - being able to function in everyday human society through direct experience of it, not a carefully curated and managed microscopic subset, that's the advantage.
I don't know of any studies (or if any could be performed, really) that demonstrate the social impact of public schools on students like this, or at least easily-identified outgroup kids. I know from anecdotal experience that in the public schools I attended that they (the semi-cultish religious kids who were not/no longer homeschooled) were not treated well, never successfully integrated socially, and disappeared from my radar very quickly after graduation. With hindsight I feel very badly about that now, and wish there some way to impact the systemic cliquish nature of public schools, especially high school. Unfortunately I lack a time machine for the kids of the past, and simply don't have answers for those going forward.
Either way, my suspicion is that public schools specifically do not offer the best (or even a much better) experience for socializing students.