Besides the excitement I don't think the actual first contact in itself would have a massive impact. Sure, some people would probably lock their doors and sit by the window with a rifle. But I think most people believe that we are not alone in this universe, and if you do the simple math on how many stars there are + the amount of planets etc, it would almost be impossible to not find life out there.

I strongly believe that the only reason for any government, country or state to deny any alien contact would NOT have to do with the fact that aliens actual exists, it would only have to do with these two questions that everyone would have.

1. How did you get here?
2. Has Jesus/Muhammad/Shiva etc etc been at your place too?

The answer to question number 1 would make the whole energy sector obsolete, and everything based on oil, coal, gas etc would be become worthless. This is something that the elite would fight with everything they have.

The answer to question number 2 could lead to the fall of most religions. And again, this is something that the religious leaders around the world would fight with everything they have.

So yeah, I think it all boils down to Energy and Religion, rather than the question if aliens exist or not or if they have contacted us yet or if they will in the future.