It sounds like you were fired for not knowing when to pick your battles, honestly. I completely understand dealing with dietary feels like trying to pull teeth. But at the same time you have to realize they are essentially working min wage, usually understaffed, to feed 150ish residents. If they stop to make a grilled cheese sandwich for Mrs Smith the food for the residents in the other wing gets cold.
They should have offered to make something else that doesn't require cooking time like a tuna salad sandwich or pb&j, but I believe you are in the wrong for telling them the resident is going to call the state on them. What you should have done is, "I'm sorry Mrs Smith, the kitchen isn't able to make you a grilled cheese right now, they can only make you x,y,z." In our facility, residents are only able to request meal alternatives up to 3ish hours before they start cooking the meal, if they want something else at dinner time it's whatever the kitchen can put together. If she is alert and this is an ongoing issue you can propose that dietary print out their meal plans a week in advance and let her pick what she wants, but it is unreasonable to demand something that specific at the last minute.
I know that you are trying to stand up for your resident but just remember 1) resident's rights don't include being able to eat whatever whenever they want 2) pick your battles. Not getting a grilled sandwich is not violating anyone's right.
It's your job to help them within reason get food they are okay with and ask management / dietary to work with them (in advanced) if they are extremely picky. I know we want it all for the residents, but it is not our job to cater to them. I'm sorry you were fired, it sounds like it was an overreaction from your management, but hey. You know better now and CNA jobs are a dime a dozen.