This movie is not about creationism vs. evolution
Because a bitter conflict between the beliefs of creationists and evolutionists is at the heart of the action of the story, it's easy to see that conflict as the story's point. Let's back up a little and take another look.
That real point is, as Drummond stresses, the right and freedom to think. He stresses over and over that his client may technically be on trial for teaching a disputed theory in violation of a state law, but he's really on trial for thinking. Drummond uses the labeling of creationism as an archaic fairy tale to stress that, for Cates or anyone else, there is more than one interpretation of the account of creation in Genesis. It may be literal truth, allegorical truth, or not true at all. This means there is a call to think about it; there are various things to compare, weigh, and from that thought process, conclude. He is saying, in part, and that it is not only permissible, but even obligatory, that people should turn away from seeing blind acceptance of any belief system as strong faith and instead to think it through. If one's thought leads back to that same belief system, that's fine, but the faith is now based on something better than buying into what one has been spoon-fed by someone else.
It is more than safe to say that if a certain set of individuals had followed that advice, the twin towers would still be standing and some 3,000 people now dead would not be.
Ultimately, Cates really did win. The jury could not possibly have properly concluded other than as it did. Cates had violated the state law; that was unquestionable. That the judge, himself a product of the same culture that had bred the vitriolic campaigns against Cates, should assess such a nearly trivial penalty shows how persuasive Drummond was. He could hardly have done more for Cates' benefit. His reaction to Drummond's statement that he intends to appeal seems more relief than challenge.
[Clarence Darrow, the defense attorney in the Scopes trial upon whom the character of Henry Drummond is based, was a famous agnostic, but did not call himself an atheist. These two terms are often confused. An atheist denies the existence of God. An agnostic doubts, but does not actually deny. They are different things. Darrow does flatly deny the more fantastical claims in the Bible, just as Drummond did when he cited the accounts of Joshua making the sun stand still and Jonah and the great fish. He maintains that the Bible was actually cobbled together from the writings of many individuals, and they often conflict. He insists that one cannot believe in God unless the God in which one believes can be visualized, and that historically that has only been possible when God was perceived anthropomorphically, a conclusion I find tenuous at best.]