I came here to write your comment and was thrilled to find it already here. As a homeschooled kid who considers myself damaged as a result, I completely agree. The OP comment is eerily similar to stuff my parents said in the 2000s-early 10s and were totally wrong about.
My parents weren't religious at all and were totally in it for academic enrichment. They were all about the "new wave of homeschooling": high-quality instructional material, study groups, plenty of socialization opportunities with other (homeschooled) kids. I turned out fine academically and probably do at least partially owe my career to it, but the social consequences for both me and my peers were severe.
The issue with playdates and study groups and the like is that the odds are good, but the goods are odd. Homeschooled kids playing with each other is an echo chamber of robotic parent-pleasers (for a while, until the break happens) who're incapable of tackling genuine social dynamics because their foremost, unbelievably deeply inculcated desire is parental praise. I feel it even now - peer approval is meaningless; only that pat on the back matters. This results in a weird simulacra of socialization: kids understand that they're supposed to have friends and social contact, but go through the motions of "this is friendship and social contact" without ever touching the real deal. Friends your parents select for you are fundamentally not real friends, and pretending they are fucks up one's ability to form genuine relationships for a long time.
Homeschooling is the ultimate egotistical project of attempting to form a living, human child - with the fractal of possible futures that implies - into a mirror of one's self. The typical liberal recognizes the abhorrence of that in a context of religious indoctrination, but is totally fine with it in a secular context. Fuck that. It's wrong for all the same reasons, and fundamentally negates the child's identity as a unique human. This is why I don't think better instructional material isn't a solution: the core problem is that one fleshed-out outlook on the nature of reality is way too little. Without multiple sources of approval and validation, it's way too easy to monopolize a kid's perspective. Again, this is realized in contexts of religious indoctrination but ignored outside of it - forcefully indoctrinating kids with a single perspective is wrong, full stop. And no, simply presenting alternative perspectives doesn't work; it'll inevitably be couched in the sort of condesencion that parents are unable to shed. Imagine your dad telling you about rock'n'roll culture: you're hardly likely to go from that to the Twisted Sister video.
Parents, of course, love this dynamic. The problem starts when those kids leave the nest and find that their parents' perspective is not the only one that matters.
The other angle is that, ime, parents who are themselves socially stunted, like mine, are unable to recognize this dynamic and insist that nothing is, or even could be, wrong. Like the parent comment, I've kept in touch with many of the kids I knew and this perspective is far from unique.
To the OP: I beg you, please don't do this. You will probably regret it for most of the rest of your life, and if you don't your kids will.