The Vatican has already, in their own way, established that extra-terrestrial life does exist, and that it is our duty to convert them . Likewise, a lot of beliefs or religions tie in with alien gods, so for those paths I don't think there would be too much shock (other than finding out that their myths / stories were true).
I guess that would have to beg the question, when alien contact is made (or rather, intelligent alien contact), would they be just another sentient species, or would they be proclaiming that they are our creators? If they're just aliens, I think a majority of people will be shocked or humbled, with a good portion of those people donning silly costumes and writing signs that read Take me to Vega or something similar. If the aliens are our gods / creators, that's when you'd have a mess of things, with rioting, religious fervor, or suppression from the governments.
As to why this would happen, if the truth were revealed, there would be no control, no restraints. Religion is about control, or else why have all these rituals and very specific guidelines that one shouldn't stray from. Should people find out there are no control measures in place anymore, their entire existence is then questioned. People without restraints are a dangerous lot.
When it comes to alien life, or the knowledge that there are aliens, I think it is best summed up in the movie Men in Black: "A person is smart. People are dumb, panicky dangerous animals and you know it." On an individual basis, people can handle the truth, but add in a mob mentality, and for some reason, all sense of reason goes right out the window. For real life examples, one only has to turn on the news to find the latest in political upheaval or racial tension, all because of one insignificant event or misunderstanding. Even when corrected or explained, the riots continue because it's just lies placed on top of lies. I wouldn't want to be anywhere near a large population center should something major and life changing take place.