My daughter is 5 years old and attends a CoE school. She played Angel Gabriel (Gabrielle?) in the Christmas play, but the songs all of the children sung weren't overly religious. In fact, they were darn funny and entertaining.
I'm a longtime Atheist who originates from the Bible Belt, so my radar to such matters is fairly sensitive.
My daughter has brought home Christian colouring material home during Christmas, which usually consists of black and white manger scenes for her to scribble on. And here and there she brings home other cultural material and little activities such as for Diwali, where there's an activity sheet included teaching her how to make her own paper lanterns for the "Festival of Lights".
For the time being, I'm working on teaching my child about the world around her and being respectful to others who are different. My husband and daughter watch "Jesus Christ Superstar" (too disco-y for me!) from time to time so she has a decent understanding about the story of Jesus. Whenever we travel and there's a large church near, my child always asks to go inside so she can admire the stained glass and the pretty statues. And she knows she has to be quiet and respectful while inside.
So for the time being we're coasting along. We also read about the Vikings, ancient Egyptians and ancient Greeks. I treat the story of Jesus in a similar fashion to the story of Icarus or Thor.
I can't claim to have all the answers. But hopefully I can direct my child in a way to make her inquisitive enough to eventually find her own path in life. And I really hope if the school(s) she attends in the future get too churchy, the level of understanding we have created at home will override the "God is the answer" information.