Is this worker’s “sincerely held” belief just that, or a disruptive attitude we don’t have to tolerate?

Q: We run a fast food restaurant and allow a female counter person to wear a religious head covering as an accommodation, despite the fact that we have a policy against head coverings that aren't provided by us. Now one of our male counter workers started coming in wearing a camouflage cap, claiming his religious idol is Phil Robertson of "Duck Dynasty." We know he is doing this out of spite, but he has told us that his "religion" is sincerely held and that he honestly subscribes to this person's views and beliefs. Can we tell him to remove his cap, but allow the woman to wear hers? – C.B., Virginia