I live in a region where this type of food is prepared in many local restaurants, so I don't go out of my way to experience this in WDW. Teppanaki is tasty, and fun to watch (if you get a talented, enthusiastic chef).
Because of how the chef cooks everything on a single grill, there is a possibility of food cross-contamination. One of my former co-workers has a shellfish allergy and when we would go out for lunch or dinner, she would mention this to the chef. He took an extra few minutes to double-clean the grill, then he would prepare the meat and veggies for everyone, with the exception of the shrimp, which he would only put on the grill after my coworker was served her food. It meant that those of us who ordered shrimp had a partial delay to our meal, but it was still fast, convenient and relatively safe. I assume Disney has a similar method of handling allergies.
Warning, don't wear sensitive or non-washable clothing -- you may leave the restaurant with a light coating of oil -- diners get "misted" sitting next to the grill.