My kids are at an independent school (ie. private) and have been there since ELC. Our school has links to the Uniting Church. Most (all??) private schools will have a link to a church, but this does not necessarily mean that they are heavily religious. My kids have chapel once a fortnight as a whole school where there is a bit of singing and someone tells a story with a moral, usually personal, not from the bible. They also have RE once a fortnight where they receive a broad based education in all religions, not just christianity. DH and I are not remotely religious, but we are very pleased for our children to learn about various religions and religious beliefs so that they can make their own decisions.

I would ask any school you were interested in about the religious education component of their curriculum.