I wouldn't completely shy away from homeschool groups who had families of more than one religion involved. The one that my family was involved with (my brother and I were both homeschooled) included families of many different beliefs. There were some that even followed American Indian Mysticism and Buddhism and other religions that you don't meet every day. They would discuss them freely but did not bring up their beliefs unless asked. The group's primary goal was to provide a wholesome education for their children. Not to just jamb religion down their kid's throats.
Look around. I'm sure you can find a few groups. Go and see how they operate and then decide if you want to be involved.
You could start with
these groups and ask for referrals if they aren't what you are looking for.
As for socially handicapping children who are homeschooled? Have you ever paid close attention to the parents themselves?? I've known socially inept children who were homeschooled and guess what - their parents were seriously lacking in social skills as well. I also have known children in public school who were picked on, bullied, or bullies and their parents were incapable of normal social interaction. I think it shows up no matter where they go to school. In general I've seen homeschooled children who interact daily with children of all ages and seem somewhat better able to interact with anyone. While children in public school who interact primarily with only their age group seem to have a harder time socializing with any other age groups. Social handicapping is negative propaganda and nothing more.
__________________
"Always learn the rules so that you can break them properly." Dalai Lama
My Karma just ran over your Dogma.