No matter what iteration of the TCB universe there is, Equestria at some point had to have made contact with Earth. And that contact had effects on the social order and response of human civilization. But how big are those effects? Well, believe it or not, the Rio scale has been made to make a loose value of how impactful contact or discovery of an extra terrestrial message to Earth would have been, based on a number of factors, like who discovered the message, how the message was presented, how far does the authentication process goes and so on.

So I thought it'd be interesting to see how impactful a message to the human race from Equestria would go down. How does it rank? Well, that varies from author to author, as they're the one's who interpret how it all went down. If you have a certain idea on how a message might have went, then click the proper boxes in the scale and see where your first contact ranked how shaken up human civilization was by it.
http://avsport.org/IAA/rioscale.htm

One other thing I found interesting while checking this out would be the guidelines & response set up by The Search for Extra terrestrial intelligence (SETI) committee, as they're the only group with protocols in regard to alien contact. No government in the world has official protocol, and most would probably defer to the SETI handbook.
http://avsport.org/IAA/protocol.htm

So, loose predictions, how would the populace react after contact from Equestria has been confirmed and announced to the world, or if ponies themselves managed to make a broad announcement to humanity?

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This was fascinating, and so I immediately applied my own take on the Bureau to the RIO scale.

The results are thus:

Up to the time of the Emergence Of Equestria, the effect of the many small interactions with earth throughout history add up to RIO 1, or Insignificant. This includes the First Contact event in the fourteenth century involving Willamus Learmont.

The Emergence, obviously, blows the lid off the scale, rating a RIO 10, Extraordinary at minimum. Honestly, I think it goes to eleven - within eight years after Emergence, not only is the entire surviving membership of the human species transformed and living in the pocket universe of Equestria, but the earth itself has ceased to exist entirely. At this point, humanity are the aliens.

Of course, by the time of the Bureaus (roughly sixty to eighty years from now) there is no SETI, and no NASA, and no nations as we know them. Thus the SETI protocols, as well as NASA and NSA protocols, would be invalid and unobserved. Mere historical oddities.

Even if such rules were in place, they would have no potency or value in the Bureau in general - not just in my stories. Equestria is there, bang, expanding in the north Pacific, and impossible to hide or contain, more than this, Celestia and her ambassadors would be essentially impossible to prevent contact with. Containment and information control would be beyond human capability.

Fortunately, considering.

I found it an interesting exercise!

I think in the case of TCB there'd be an extra level of freakout just because of the nature of the civilization contacted. We're primed to accept little gray dudes with big heads or hentai tentacle monsters or Dysonian space robots or enigmatic Bowie-esque Star Men or psychedelic energy swirls, but we meet another form of intelligent life and it's magical rainbow-colored ponies in a high fantasy world? That would blow a lotta people's minds. Some people would jangle their beads and be like "I knew all that stuff was real!" but everyone else would be like, "This has got to be a joke or a disguise, right?"

It's a bit like a mirror image of the problem faced by the Overlords in Childhood's End, only instead of the aliens looking exactly like Satan it's something so familiarly happy and reassuring that you know you're not getting the whole story.