It'd be selfish to think we are the only beings occupying the universe and I do think the government knows a lot more about ET life than they disclose to the public, but I can't blame them, imagine what would happen to religion if the world was told that aliens exist...
Religions always have a way to counter a argument. Religions wouldn't be a problem, the reactions of the people will, I also don't really think it would create so much chaos. Mostly it will be curiosity added with a little bit of fear