I haven't watched the movie, but I read the premise online. Therefore, sorry if I am speaking incorrectly about it. The problem with most films like this that bash you over the head with a message, regardless of the actual message, is that they often create some of the most absurd strawmen imaginable in order to support their points. While I'm sure there are a few cherry picked examples we could all think of where the contrary is true, no dean would ever stand for a professor, even tenured, requiring students to sign a declaration that God doesn't exist in order to receive a passing grade. And has been already stated, Nietzsche's statement that God is dead (which is what I assume inspired the film's title and the declaration narrative) was not a metaphysical statement; it was a statement about changing cultural values and laid the foundation for his description of the ubermensch. Max Weber made a similar observation about rationalization replacing theocratic values as society became more industrialized.
Also, yes there is a somewhat mistrust of academics and intellectualism - at least in America - that manifests in certain facets of popular discourse and culture...which is somewhat funny, since academic thought leaders,like Cornell West and Noam Chomsky, who often serve as the poster boys for dangerous academics, are really the small minority. While a few academics do use their job stature to bully students for holding differing views, anecdotally speaking, I find that most professors respect a student who holds a contrary view and can defend it well. The issue is that you often find gunners (yes, gunners can exist in undergrad too) who make it a mission to debate the professor because that person is confronted with a viewpoint that has differed from the one he or she has held their entire life. I recall serving as a grad assistant for my supervisor's senior-level men's studies course that was taught from a constructionist viewpoint. One student was constantly adversarial in his weekly papers with the material. That's fine, but he was constantly prone to fallacious thinking in attempts to support his point and somehow attempt to paint my supervisor as inept due to an ideological axe to grind. He probably thought I was pointing out the holes in his thinking when went over his papers due to ideological differences I had with his perspective, but my interest was in teaching students to posit a cogent argument. But I digress. My point is that anytime I hear someone like David Horowitz complaining that students are being marginalized for unpopular views, I take it with a grain of salt. Often, it's not that students have a differing view that causes the issues - it's their inability to cogently defend it.