I'll be upfront and say I've homeschooled my four kids since my oldest was 3 years old and I saw her eyes light up when I taught her to read. I love teaching, I love spending time with my kids, and I love learning myself, so homeschool is the perfect lifestyle for our family.
I am just one homeschooler speaking, though, and as a community we are quite an eclectic bunch! I know plenty of completely secular homeschoolers and others who would list religion as their number one reason to homeschool. To put every homeschooler into one bucket would be a vast oversimplification.
I believe it's a fundamental right of a parent to raise and educate their children in the way they feel is best. Yes, there are extreme cases of abuse and neglect (independent of educational choices) in which society is obligated to step in and parental rights are justly revoked. But while I think you are spot on that homeschoolers tend to be more influenced by family than by peers, I don't share your concern that parents' increased influence over children is inherently any more dangerous than a 100% standardized government-dictated education. In either case the fear stems from the possibility of the extreme, not of the practice in general. Lived out in thousands of homes and in thousands of schools, you get a pretty wide distribution of "success" in both methods of schooling. It might help to know what you're referring to when you say "the betterment of society?"
In our home, much of what our kids already (and hopefully will continue to) give back to society stems from what I suspect you might label as religious propaganda: treating others as children of God, allowing others opportunities to change, being honest, being diligent, being chaste, being good stewards of what they've been given in health and resources, visiting the sick and the afflicted, treating life as a gift, etc.
I also think you're creating a false dichotomy here when you paint a picture that religion precludes critical thinking. I'd consider myself a very religious person yet my background includes a degree in chemistry and the favorite subjects at our house are science and math. Teaching my kids how to think is one of the main aims in our homeschool! Separate your feelings about religion from your feelings about homeschool and where does that leave you? Certainly not all homeschoolers are religious, and certainly not all children who go to public school are without religious education, and certainly religious people as a whole aren't a detriment to society.
There are plenty of other assumptions in your question that muddy the water. Here's one: That racism comes more from parents than from peers.
I don't homeschool because I believe it's better for society, though from where I sit it strikes me as probably a net neutral. In the past, the majority of homeschoolers were seeking to get away from something they distrusted, but the surge in popularity in the last decade has been skewed towards those seeking a better educational experience for their kids given the limitations of the public education system. In general, I think we see that where we have engaged parents, strong family ties, and a focus on education children grow up far more likely to be thoughtful, contributing citizens. Homeschoolers certainly don't have a monopoly on this atmosphere or on involved parents, of course, but especially in recent years the choice to homeschool more often than not reflects a willingness to sacrifice on the part of one or both parents in order to improve the education of their child(ren). They may have different views on creation vs. evolution than you (as I do) but I think you'd be hard pressed to rank that high among the ills of society. Hatred? Yes. Indolence? Yes. Entitlement? Yes. Different understanding of the origins of man? Meh.
I'd also add here that "accepted science" has changed over and over again as we deepen and broaden our understanding and powers of observation. My children and I are reading a biography of Sir Isaac Newton right now and discussing how little he knew and how little we likely still know of all that can be known. I think a great education (both religious and secular) acknowledges that.