You're rather neglecting the past thousand years or so where the Catholic Church would have you executed for thinking the earth wasn't flat. And let's not even mention their issue with women, witch hunts, and of course the Inquisition.

And you're somewhat misleadingly misrepresenting that Wikipedia article. It actually says that the no-conflict position is an unofficial stance of the Vatican.

It also (rather importantly neglected by your comment) says that their position is that humans are indeed special and need the existence of god. That's rather a conceited view of our species, but then this is coming from the same organization that spent much of the 13th century burning whole french villages...