Re: even in western mainstream education the "religious education" is there.
And rightly so. Religion is a massive part of human life and has been for thousands of years. To not educate children in religion because you're not religious is like not teaching them history because you're not from the past or not teaching them geography because they don't live on a mountain.
The problem here is that R.E. is supposed to teach you ABOUT religion, not preach religion at you. I'd be interested to see exactly what was taught in that lesson, did your daughter just love the story and the songs or was the teacher trying to convince her that Christianity is the one true faith?
Sounds like you'd add a bit of balance as a governor, but don't get carried away. Arguing from a position of knowledge is always better.