What is a word for food preferences?

This is usually called diet, or if you want to be more wordy dietary preferences.

Since you're including "hard" things like allergies, as well as "soft" things like likes and dislikes, I'd go with the "hard" and use the term requirements.

What are Johnny's food requirements?

As you're talking about both things like allergies and sensitivies, and preferences, I'm not aware of a single word that encompasses both. Words like "taste" and "dietary preferences" only connote the "voluntary" things to my mind. Words like "dietary constraints" only connote the "involuntary" things.

Simply saying "Bob's diet", even aside from the possible confusion with weight loss program, doesn't convey that this is either what he likes to eat or that it excludes things that cause him problems. It simply indicates that this is what he DOES eat. I don't think it would be at all paradoxical to say, "I spent a week stuck in this isolated place where my diet was limited to crackers and milk, which was a real problem because I hate crackers and I'm lactose intolerant." Just because I don't like something or even that I'm allergic to it doesn't mean that I didn't eat it, i.e. that it's not part of my "diet".

I think that if you want to clearly express this idea, you would have to say "his tastes and dietary constraints" or some similar phrase.

All that said, if you're just looking for a heading or title to put on a report or computer screen, where it doesn't have to fully explain what you mean but just not be inapplicable, I think "Diet" would cut it.