We homeschool after both kids went to public school kindergarten, and my kids have friends who attend public schools. One public-schooled neighbor (who was my son's friend friend while he was in public school) we see almost daily. I call him "my third son" because he's at our house so much. It hasn't been a problem.
If you're talking about someone who doesn't live within walking distance, then I'd still say that it is absolutely possible to maintain friendships with kids in other educational situations *if* you and the parents of the other kids are willing to make it work. It's more of a commitment, but if they attend the same neighborhood school now, then presumably the other kid doesn't live more than a few miles from your house. If you're willing to pick up and drop off the kid, what parent would say no to playdates?
Do you know the other family? Could you talk to them about your plans and explain that you want to nurture the kids' friendship? Most people will respond positively when you say nice things about their kids.
Personally, I would not recommend staying in a school situation that you feel is a bad fit for the sake of one friendship. My highly social son hasn't missed his old school. We still have playdates with his school buddies. It's working great. He's as happy as a clam.
Does your child have any homeschooling friends yet? That would help with the transition. We had one when we started homeschooling our first child (and had many more by the time we decided to homeschool the second one, of course), and more than anything that homeschooling friendship was a security blanket for *me*. It assured me that we wouldn't be all alone all day every day.
And just to be clear, my fears were way off base: we definitely weren't alone. My biggest problem with homeschooling the first year was that we were being social *so much of the time* that it wore me out! The kids did fine with it and made friends easily, but I was over-socialized and came to see that time alone was a need for me, and one that had to be balanced with the kids' needs for social time. But the kids did absolutely fine.
I'd explore the chances of keepng the friendship alive outside of school before changing your homeschooling plans. It isn't really that hard to do if the other family is up for it.
