It feeds confirmation bias.
Last I saw anybody doing research--it's been quite a few years--about half left homeschooled for reasons of religion and morality (put them in the "conservative" camp) and about half for reasons of rigor (let's put them in the "liberal" camp). (Note that "morality" can include those on the left-side of the political divide--"I want a green curriculum" and more than one religious "nut" has high academic standards.)
Same for materials. The few homeschoolers I personally knew well had either religious nutjob curricula or some really good curricula. In one case the parents pulled their daughter with a D- at the end of 9th grade out of school. A year later, when she went back to public school for her junior year she had to take placement exams to make sure she hadn't, as the principle put it, "lost too much time." The young woman easily placed into all senior classes. That is, in one year of homeschooling she went from nearly failing to being a year ahead and skipped 11th grade.
Same for "vigilant". Some religious nutjobs are really vigilant. Some "I want my kids to learn something" parents both work and their kids slack off, but the parents can't do much about it. Lots of diversity everywhere.
= new reply since forum marked as read