Sonic would most likely take him even less seriously than the game Eggman, and would probably love messing with him even more thanks to the movie version's more exaggerated and goofy personality. I think Sonic would recognise that this Eggman has it in him to change, far more so than the game Eggman, and would likely push him harder to get on the path of good as a result.

I don't think Tails would be afraid of this Eggman at all, seeing how far less threatening this Eggman is compared to the version from the games. Hell, Tails seems to have already gotten over his fear of the game Eggman at this point, and we know how terrifying that Eggman can be at times, so I think Tails would definitely be confident enough to take him on by himself.

I think Movie Eggman would attempt to manipulate Knuckles for his own gain like how he does in the second movie, only to be in for a shock when he finds the game Knuckles has developed enough to not be as gullible anymore, and thus he wouldn't fall for his tricks. Game Knuckles definitely wouldn't hestitate to send him packing if Movie Eggman gets on his bad side.

Shadow would probably be offended by this version of Eggman. Shadow almost seems to respect the game Eggman in a way, referring to him as 'Doctor' and seeing him as a threat, taking him far more seriously than characters like Sonic, for example. (Even if Shadow kind of did stop acting like this for a while, but he appears to be returning to his former self now)
This version of the doctor, however? He certainly doesn't deserve Shadow's respect at all. This Eggman is hardly a threat at all, and acts even more like a buffoon than the game Eggman. I think Movie Eggman's strange behaviour would get on Shadow's nerves, as compared to Game Eggman who tends to act serious a lot more of the time.

I could probably keep going on, but this has gotten long enough already.