The Driver of science is the Scientific Method. Early scientists merely thought their usage of the Scientific Method would confirm things about Reality that they were taught by Religion. That's all, it's not a Driver, it was just people with pre-conceptions given to them by Religion. It didn't take long before they realized their pre-conceptions were incorrect.
I just don't think it's as simple as that. The 'scientific method' didn't just appear one day, as a sudden revelation. Indeed it seems more a retrospective rationalisation of what people had been doing for some time without consciously deciding on it.
To start thinking in a 'scientific' way requires all kinds of intellectual and physical preconditions. Religion was one of the things that created those conditions.
I can't really sustain an argument over it because I've forgotten all the things I read about it in the past (like climbing a ladder that then falls over leaving you wondering how you got here, I just know I at some point decided I didn't agree with what you say here, even if I don't quite know why any more).
Besides, while I know I'm not being at all convincing, it doesn't seem that important an issue given where we are now. It's a matter for historians, really.