Yeah, I think it's a bit odd that Tony Stark would side with registration, but I think it sorta makes sense in the context of these movies. I think they probably could've done it a little better, but I think it's sorta the natural progression of the character.
A lot of people point to the fact that Tony stands in front of the government in Iron Man 2 and tells them that they can't have his property. That he's a private citizen and that the government is infringing on his rights. And, yes, that's a huge turn from where he is in Civil War, but people forget that Iron Man 2 is the third movie in the MCU. In the mean time:
- Tony learns that there are aliens (Chitauri) and that Norse gods are real (Thor/Loki).
- He fights an army of these creatures, almost dying in the process.
- Almost dying gives him panic attacks/PTSD, and it causes him to build tons and tons of suits to feel safe.
- When this doesn't work, he decides to build Ultron and the Iron Legion. He decides that he might not be smart/strong enough to defend the Earth, but he's smart/strong enough to build something that can.
- Once again, this blows up in his face.
The man who faces the government in Iron Man 2 has built this kickass suit of armor, has dominated every foe he's faced, has "privatized world peace," and has his dream girl. And while he wins in the end in Iron Man 3 and both Avengers movies, it comes at a great cost. He almost dies, Pepper almost dies, his arrogance has turned against him (literally) in all three movies (the Stark Tower becomes the conduit for the Chitauri, the Mandarin is borne from his arrogant past, and Ultron his literally his baby).
So I saw him agreeing with the Sokovia Accords as finally admitting that he can't do everything on his own. But it's still the same guy because he still thinks he's smarter than everyone else, and every fight in this movie is basically him trying to convince Cap that he's right about whatever decision he's made.
And I think one of the key ideas is that he's lost Pepper. In Age of Ultron, they explain away Gweneth Paltrow's absence by saying that Pepper is away or something (same with Natalie Portman's Jane Foster). The truth is that there was no place for Pepper in an already-bloated movie. And the same was true of a very-long Civil War movie. And, again, they could've explained her away with a throw-away line. But the fact is that Pepper is gone - and Tony's lost something else. It's more doubt to throw in Tony's face and more reason why he might be willing to accept oversight.
(And what's funny is that Tony still basically works alone, with no oversight, the entire movie. So it's still basically in character).
And Steve's stuff make's sense too. He wants to be a good little soldier, but in every movie, the government has been evil. SHIELD was secretly run by HYDRA. Nick Fury was spying on him. Then SHIELD disbands, and he starts working for the Avengers. But then Tony builds an evil robot that they all have to fight. So he can't really trust the Avengers either.
Because, at the core of things, Steve is a soldier. It was easy in World War II because Germany and HYDRA were obviously evil. There was a clear indication of who was good and who was bad. And in each movie, Steve has to question who to trust. Who's the good guys and who's the bad guys.
And, yet, Steve is still a trusting guy. He forms a quick bond and instantly trusts Falcon after knowing him for a very short time in Winter Soldier. He instantly trusts Ant-Man right before one of the biggest battles of his life without knowing anything about him. And, of course, he's firmly loyal to Bucky despite everyone else turning on him.
That's what I like about the MCU. Yeah, they're kids movies without a whole lot of deep thought or character development., But after movie after movie, I really do think they're allowing these characters to evolve and change. I think Civil War the movie might be more earned than Civil War the comic. And even if a lot of the stuff I wrote wasn't explicitly stated (or even intended), the pieces fit together well enough that it does feel earned.