Hmm, that wasn't my experience. There is a huge variation in the family types who are home schooling in the Bay Area, it runs the gamut. Two of the kids in the Reikes class were homeless, their Mom was doing this because while she was homeless she did not want here kids to get behind in their education, and California has some really strict rules about letting your kids go to a public school if you don't have an address in the district. Perhaps the biggest cohort were kids where the parents had an issue[1] with the public schools but didn't have the resources or desire to send their kids to private school. I do know that there was a group who leaned more toward the creationist side of things but that wasn't the groups in our circle so I can't say much about them other than that you could find them if you wanted to.
"It is already known that the most important factor in whether a kid learns or not is their home situation."
My experience would support that hypothesis. Of all the kids I've known over my life those who had parents that were supportive of their educational goals did better than those whose parents were absent or destructive. That said though, it didn't change the fact that for kids who were otherwise nominal (reasonable support from parents, no major mental health issues) learned a lot (and I believe more) in their home school environment than they would have had they gone to public school.
[1] Issues ranged from teachers who were 'bad', district policies (no pocket knives allowed), school choice in their district (gang issues), and 'bad influences' (drug use or sexual experimentation).
