My wife are secular homeschoolers and have homeschooled our 3 kids: 10,8,5 for 5 years. We use outschool regularly, its a great platform to introduce random topics. I would invest in it honestly. AMA I guess
What were the primary motivations for homeschooling? Cultural? Political? Quality? Access? Also how do you go about socializing them? I've been considering it myself
Based on that limited observation, I think that the socialism of homeschool kids depends on the kids and their parents in the same way as any other aspect of homeschooling: If the parents are reasonably social, they will find ways to get their kids involved in social things, and their kids will be social too.
If the parents are reclusive, or inclined to isolate themselves from mainstream society for whatever reason, this will also be reflected in their kids. What may seem like a negative outcome of homeschooling could just be a matter of kids resembling their parents. And it wouldn't shock me if genetics plays a role.