> So, if humans find out they were a byproduct of randomness,
Literally nobody believes this.
If we did find out we were a product of randomness, we'd all have been proven wrong. The theists who think we were designed and those (theists and atheists alike) who think we were the result of an evolutionary process.
That said, many would simply reject the evidence, no matter how clear, continue to hold their previous belief and act by it, especially if prescribed by a religious authority to do so. Their behavior wouldn't be any different than it currently is.
I don't think it would have dramatic effects on those who do accept the evidence, except those whose previous career or behavior related to that specific topic (i.e. both religious figures and evolutionary biologists would be in a difficult spot).
But even if so, it wouldn't matter. We should evaluate the truth value of a statement independently of how we or others would react to it. To do otherwise is wishful thinking.