If/when an extraterrestrial civilization ever decides to make itself generally known to humanity it will be a complete shock. If it is even possible to comprehend the aliens at all. I know I am making unwarranted assumptions here, but I have to start somewhere. So these are my assumptions:
Quite aside from the appearance of the ETs, they will challenge everything we think we know about religion, science, and government.
I wonder how any government they may have, or may not have, will affect our own. Being completely different from us, their methods of getting along may not even have any application to our situation. Personally, I would hope they have advanced beyond the need for any government other than self-government. That is my bias. What if they are socialists or an even worse kind of slave? Could our ideas of liberty influence them at all? Would it be like bacteria giving our philosophers ideas on how to organize civilization? What if they have no "self"? Or what if their idea of "self" is that each individual is basically at war with every other individual? I think that is very unlikely. I would think that in order to have technology that enables them to travel to earth, they would be rather cooperative. That is not a certainty.