We wouldn't know what the aliens are really like, and they wouldn't know what we are like. Failing that, and contact with the aliens military is made, the first barrier to communication is simple yet significant there would be some sort of language barrier. If they don't show any signs of suspecting we exist, I suppose humans would try to discreetly study the aliens as much as possible. More than likely it would be whatever military the aliens have that would discover us first if they have the tech to do so. It might be better to consider this from the opposite perspective: If we one day a) discover an alien species and have some method of travelling there and communicating (stealthily), what would happen? Should select members of whatever alien rulers discover our existence, why would they hide us from the alien population? Proving that claim would require enormous amounts of evidence: have it? 'War of the worlds' was a very localized, globally unimportant thing. Without dogmas to keep stupid people in order, they'd perhaps start wrecking the society. Majority of people are playing nice 'because the holy book says so', not because they feel like it's a good thing to do.

I don't know about the consequences, but it would be huge. It would be the ultimate 'the emperor has no clothes' thing. The number of people who claim to be members of those religions (mind that's not the same as 'religious people') would probably experience a massive drop and that would create large changes in the society on the global scale. It would rock the dogmas and, as always, they'd try to fix it by accomodating their lies to fit the new world, just like they did with evolution, Solar system, etc.

It's an actual meme in the very sense of the word.Ībrahamic religions would get a large punch in the balls if proof of intelligent life outside Earth is ever found. The whole alien meme is a commercial product and it was highly profitable. The whole 'aliens are visiting us' thing got big when science fiction of the 50's started mentioning it.

So.seeing that we're not yet snuffed, or dealing with an alien contact fiasco, then so far either we've encountered wise and careful aliens, or none at all. No sense showing themselves to us, monologue-ing, etc. On the other hand, if aliens had bad intent we'd suddenly find a large rock or ice ball headed our way, then POOF we're snuffed. If they're not particularly bright but well meaning, then first contact may be a messy affair, probably more to worry about from terrified humans than aliens. Assuming the aliens were intelligent enough to offer us something of value, they would, like wise adults, either stay out of the way or have a plan to reveal themselves in a manner that minimizes danger to individuals or society.

Government, military or business leaders might not be the best choice. If these aliens decide they want to help us, and they went ahead and made contact with some humans, they'd have to choose very carefully.

Kerbal space program 2 aliens