I was going to suggest you let them take turns choosing which cup/plate they use. But then thought this was too much attention too. I suggest that you not tolerate whining. Tell the 5 yo ahead of time that if she chooses to whine, make a fuss, then she'lll not get any juice, dinner and will go to her room until she calm down and come back in a neutral to good mood. Ignore the 2 yo. Explain, during a calm time what will happen and then make it happen every time.
The 2 yo wouldn't understand that process. I suggest that this is another form of sibling rivalry. The two are feeding off each other. When you remove one you've changed the dynamics.
You could start out by simply ignoring the whining. Tell them, you can't hear them when they whine. It will be tough but if you can consistently ignore them over a week or two I suggest that they'll learn that whining gets them no attention which is what they're after. If you have to leave the room to catch your breath. Return once you've reinforced your resolve.
If you're not having this difficulty with the two of them in other aspects of your life, then I'd get inexpensive plastic plates and cups all the same color and put the character ones away.
After ;your SWH Seems like you want to set the table with matching character dishes and cutlery. Why would you need 6 set? And why would your continue to provide character plates, etc.? Seems like the consequences of not cooperating with how you set the table would be to have plain and inexpensive settings. If using character sets is important to you then use the character sets you have for treats or rewards.
And after your added note. You can stop the fights over colors by just telling them this is what they get. I think you're over thinking this situation and turning it into a problem. Sounds like you want perfection when you need to be the mom and set boundaries. i.e. you like them have character dishes and specific colors. It's not working so try something different.
I do not agree that you should take away the food if they whine about the dishes. Give them the food on the plate and let them either eat it or not. Do not accept whining. Set your boundary at no whining and stick with it. You are doing them a disfavor by trying to make them happy all of the time. You just cannot do it and are setting yourself and them up for continued disappointment. Tell them what they get and be done with it until they're older and can learn about sharing. Yes, your 5 yo could learn that now but youre 2 yo can't. So take charge!