In Agents of S.H.I.E.L.D., the President announced the creation of the ATCU led by Rosaling Price to catch and contain or eliminate Inhumans. It was the same President from Iron Man 3. It has been reported that neither Maria Hill or Nick Fury are set to appear in Civil War, which means likely possibility of S.H.I.E.L.D. going public might not happen. If they go public it would be sometime during Season 3 as not only are they faced with the ATCU and Price but HYDRA as well as they try to find other Inhumans.
But isn't that just the U.S. President? SHIELD is no longer attached to any one government even if they did primarily operate within the U.S. before, where the Triskelion was based. Now that they're airborne, they don't have any national sovereignty issues, so going public may make them enemies of the governments that oppose them but those governments don't have the authority to just shut them down. If they come knocking on the door, of course, that's a different story. They just have to be careful until things settle down and an open dialogue and trust can be established.
This really is the best opportunity to tie in the movie and TV-verses but that won't happen. As it is it will probably be hard enough to get everything they want into the runtime of just the movie itself, never mind the show and all the stuff they're doing independent of the film. I mean, someone really needs to just go up in front of a microphone and say, "Listen, people, this isn't Doctor Who where you can still get away with not believing in aliens even when they crash a ship into Big Ben, they're real and they've attacked numerous times and guess what else? They tinkered with our ancestral DNA so now you or your own children have the potential to become superhuman, perhaps dangerously so. Your fear, hatred and bigotry aren't going to help keep this from knocking on your door so let's all come up with a game plan that does more to help than hurt, or this could go wrong in so many ways it would make your head spin."