Failing to address a customer's allergies can lead to a civil lawsuit. Once the customer informs you, whether in written form or verbally, of his/her allergies, you are now legally accountable for using this information for future decisions. For example, if you are a waiter and a customer informs you before ordering that he is allergic to shrimp, you are accountable for telling the customer which dishes on the menu have shrimp. It is also your duty to inform the chef or line cook of the customer's allergies if you are not familiar with the ingredients of the dish.
However, it is also important that the customer articulates his medical conditions to you in a clear manner. If not, there is a large possibility that you will not be held accountable in a court of law if you can prove that the customer did not communicate to you his/her allergies in a clear manner.
In terms of intolerance and sensitivities, the legal consequences of failing to address these is not as well-defined as failing to address allergies. This is because allergic reactions are physical symptoms and can be evaluated by medical professionals. Additionally, some allergic reactions could have fatal consequences. However, a customer could still filed a lawsuit citing "emotional distress" as their basis for taking legal action.