I know this thread is two years old, but I wanted to post the solution in case anyone else comes across it.
The problem: The account that owns the game is playing on a secondary (non-primary) switch console.
The symptom: No other switch account is allowed to play local multiplayer. Attempting to hit "Y" to change the account will result in an error message.
The solution: You must make the console you're attempting to play on your primary console. Once the console has been set to primary, other switch profiles will be able to play local multiplayer (by pressing "Y")
The steps to achieve the solution:
1) Log onto the account's (that purchased Castle Crashers) primary console. The primary console is defined as the first console a given account logs into the Nintendo E-shop.
2) Log onto the Nintendo E-shop with said account.
3) Select the account's picture in the upper right corner of the E-shop.
4) Under "Account settings" (your profile picture selected in the left side of the screen) scroll down on the right side of the screen until you reach "Primary Console". For me, this setting is right under my password/email section.
5) Select "De-register" primary console. Confirm your selection.
6) On the console that you wish to play Castle Crashers, log into the Nintendo E-shop with the account that owns the game.
7) Log out of Nintendo E-shop, and restart Castle Crashers.
You have now set the new console as the primary console of the account which owns the game and you should be able to load AND SAVE other profiles in tandem with the primary account.
NOTE: If you no longer have access to the primary console of the account which purchased the game, Nintendo provides a method for you to remotely change the primary console. You are only allowed to perform this operation once per year or six months, I think. See Nintendo's guide for this process.
I hope this helps someone. Wish people posted their solutions more.