If some alien force with incomprehensible power and an unknown agenda, has been acting at will on Earth for who knows how long, then humans are not the dominant form of intelligent life on Earth, and have possibly never been in charge of their own destiny. What are we, then? Animals in a zoo? Specimens in a lab? Playthings? Food? If a government admits there's nothing they can do about it, they're basically ceding their own sovereignty to this alien power. A state that can't police its own borders or airspace isn't credible. No one would trust it.
This is just assuming one particular scenario happens to be true. If alien contact turned out to be a unique event, then people's reactions might be different. Given how prevalent the topic is in science fiction and popular culture, it could be argued that humanity has been indoctrinated against the possibility. But even then, knowing that's just fiction makes it comfortable.
But the shock of actually learning we're not alone would be an event of such import, we would need to restart the calendar and consider it a new age, year zero Anno Contactum (or whatever). I think humanity would experience the collective form of a fight or flight response - a mortal animal fear at discovering the sudden gaze of a predator in the tall grass.
To paraphase Agent Kay, "A person is smart. People are dumb, panicky dangerous animals and you know it."