My daughter's diet is gluten free, dairy free, and soy free. We have found that Royal Caribbean and Celebrity makes it much easier to deal with her dietary restrictions. And dietary restrictions are so common now, it is even easier to deal with.
In the MDR, talk to your Head Waiter the first night. You can go over the next nights menu and special order food. You can get simple substitutions like swapping rice for mashed potatoes, or have them cook something completely different. There is now a full time chef on board who only deals with special requests. Another note: anyone can special order food. On Beef Stroganoff/tuna night, I have been ordering fried shrimp or fish because nothing on there looks that appealing.
In the Windjammer, there will be a chef/supervisor nearby who can answer all your questions. This is much improved, where before, they frequently had to go find a chef to answer questions. The biggest issues at a self serve buffet is that other diners will contaminate food.