Although both plans recommend two dairy servings a day (for the average person), there are no "required" or "restricted" foods on the flex plan. You eat what you want to eat as long as you do so within your points range. I can't imagine that it would be hard to follow a dairy free plan.
I'm not following core, because it does have some restrictions that don't appeal to me (e.g., using only fat-free dairy products and salad dressings), but from what I know of the core plan, I don't think there's any requirement for you to consume dairy on that plan, either.
I know there are tips for people who are vegetarian. I've never really noticed if there are tips for other types of food sensitivities, but if there aren't that's what leaders are for. You can always ask them for guidance. In my opinion, WW is about eating moderate portions of the foods you want to eat. If there's something you don't like or are allegic to, you just eat something else. It's that simple.
Hope that helps,
Josie