I only know secular home schoolers, but I haven’t seen this. These kids are exceptionally well-rounded socially, spend time out in society meeting real people, and their parents usually allow them much more agency than the average kid. IME, I have seen it in parents and children who attend public and private schools. This is the era of overprotective helicopter parenting, and those kids spend 7 hours in school (usually with people just like them), the rest of their free time is with a sitter/afterschool program, their parent, or attending structured activities with their peers from school. I rarely see the kids in my neighborhood (a white, majority Irish-Catholic one where most of the kids go to the local Catholic school) outside their houses. At least when I was a kid, living in a small town as we did I could spend hours out on my bike exploring.
Also, as you probably know, like gravitates to like for kids as well as older people. I went to several somewhat diverse public school systems; in each of them my best friends were all white, nerdy kids with above average intelligence and parents who were disproportionately academics (as were mine). That’s not to say I wasn’t friendly with all sorts of people, but school taught me is that I only had much in common with a very small subset. I had some social problems later in life because I didn’t learn how to interact very well with non-nerds, or people outside my peer group. I couldn’t make small talk and was intimidated by anyone older than me. This cleared up with a year or so of working at a real job with a variety of people. However I still only have nerdy, smart, mostly academic friends (even though I’m a high-school drop-out, I like to learn as do all my friends, and most of them have degrees by this point), most of whom come from the same kind of background as I do.
I guess what I am saying is that if you don’t make a deliberate effort to give your child varied experiences and familiarize them with all kinds of people, whether they attend school or not - they are not going to become well-rounded from spending 7 hours per day in a building with 1000 kids from your immediate area.
