Is there a way to fix the Talk/Cancel bug in Shantae with an Xbox 360 controller?
As discussed above it's not really a bug - but the knowledge of that won't comfort you at all.
It turns out that there is a way: you can use a hex editor to hack control settings straight into the save file. It's warned that it may cause some issues, but then again so does not being able to navigate menus. This comes from this post
on the Steam forums. Basically you just find it and swap the bytes at offsets x560 and x570.
I tried it, it works. No glitches so far, but I'm just starting the game.
EDIT: Just finished the game with this hack. The mentioned glitches are not bad at all. Since jump and talk now share the button, Shantae often does a little jump when talking to an NPC, this is entirely cosmetic. She also can't really jump when an NPC is right next to her, because she'll end up talking to them instead. This slightly complicates getting to rooftops in the town to check if the people have anything funny to say, but it won't cause actual problems. If you are bothered by the controls, you'll think it a worthy exchange.