People lie in polls, but unless there is some overwhelming reason to do so in one direction or another one has to assume the data to be reasonably valid. Most people I know who school their kids for religious reasons, private or homeschool, freely admit that o be a major reason. Alternatively, most homeschoolers I have met - like me - do not have religion as the primary factor or even as a factor. If you do not want to accept the survey as reasonably valid, then we have anecdotal evidence only, and I know it is not true in my case, and I think it's a safe bet I know more homeschoolers than you do, unless you have some specific background with it you have not detailed, since homeschoolers tend to talk to each other a lot when we find out the other person did too. And my experience - extensive - is that minority of parents have religion as a major reason, and that most of those also have many or all of the same reasons those who didn't cite religious reasons have.