This is something that I do have experience with

My husband and I are not religious although we have looked into a Unitarian church in town. The public school that DS was assigned to ranks very low on test scores and from what I've heard is not a great school so we looked into private schools. We picked a Catholic school that seemed like it would work well for him. I got my first inkling of bad things to come when on his first day I overhead a kid asking the principal why it was raining outside and he said because God wants it to rain. I knew my son would question that to no end.
He didn't do well in that school and their attitude was because it was a private school they could kick him out at any time and didn't have to put up with his differences. When he started questioning God about the second week I was really nervous but luckily I convinced him to not talk about that at school. I knew that would cause even more problems. We weren't required to attend church there or anything like that but in the upper grades I think it's a requirement. It was a bad experience for all of us so I put him in a public Montessori for this year.
That being said I'm considering a private Episcopalian school for this coming year. They seem to encourage grade skips for kids that need them and they don't seem to focus on religion as much as the Catholic school did. I think that in my case I can overlook the religion aspect if the school is a good fit.
How do you feel about the religious aspect of it? I want DS to learn about lots of different religions so when he's older he can decide what he believes but I don't want him to be forced to believe a certain thing because he attends a certain school.
Also, if you put your kid in a private school and don't like it will the public school accept him into 1st next year?