My guess is yes, but I have no direct evidence of that. The thing I think I can say with certainty is that there's a long tail of parental effects on socialization for homeschooled kids. Very severely conservative or religious parents are very likely to have kids with these problems to a moderate or strong degree. And quite a few homeschooling parents in the United States are like this - you might very well be in a liberal or urban bubble if you don't see this in your local homeschooling community.
> My own kids seem, in contrast, to have gotten more out of clubs fitted in around schooling
I don't mean to sound like I'm totally opposed to homeschooling. I actually think it can be much better than public schools with the right parents, the right environment, the right amount of money, and so on. I'm not clear on exactly how old your kids are, but I would warn that I do think it's significantly harder to encourage the best social development once they become teenagers.
> a couple of the teachers
By "teachers" I assume this means you are hiring outside instructors or doing co-op classes with other homeschooling families where your kids and there kids are being taught at the same time. This is a very different kind of experience and not what I referred to as "full homeschooling" in another comment in this thread.
We don't do education otherwise, we wanted to flexischool (UK) but the teachers vetoed it. However, we know quite a few families who homeschool and they have an incredible bunch of socially active, artistically skilled, intellectually capable kids. Socially, they seem to be ahead of other groups, to me, because (I contend) they get/got a lot of inter-age interaction. There's probably a lot of selection effects too.
My own kids seem, in contrast, to have gotten more out of clubs fitted in around schooling, as opposed to their socially fulfilling time seeming to be more co-terminous with educational experience.
One thing I'm concerned about with school is that up until 12yo the kids only regular day-time contact with men is the janitor ... it's a slightly orthogonal issue, but I guess in general "you can't pick your teachers" applies for most people and even in our pretty nice neighborhood a couple of the teachers have had lasting negative effects on our kids.