My understanding is the US was founded by especially religious Puritans, and perhaps being an ocean away from the late-renaissance Europe helped stifle progressive thinking further.
Since then, due mainly in part to having such a spread out population forging their own way in new lands (and also possibly spurred on from winning independence), it's had strong ideals of rugged individualism. This inherent selfish nature has led to a rise in conservatism much stronger than that in many comparable places, which in turn has lead to a hierarchical, winning-at-all-cost mentality. A population is easier to subjugate if it's uneducated, hence the anti-science push.
I'm from the UK and the big bang theory is widely accepted, as far as I can tell. Creationism as an opposition to the BBT isn't very openly touted by many, at least.
I'm not sure how to answer your last question. Maybe ensure the scientific method is thoroughly explained and engrained from a young age — make sure it's understood that it's never a question of devout belief, but rather about data and falsifiability. And don't teach religion as fact... although good luck implementing that.