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By appearance, do you mean attire, or just how you look?
If you mean attire, then yes they should. It is a business, and the owners should be allowed to do whatever they want to protect their investment and run a successful business. If they feel a certain attire might cause a loss of business, then the owners should be allowed to refuse entry. If they had open weeping sores it would be a health hazard so the owners would be ok in refusing entry.
If you mean looks, not thin enough, pimply, scarred, tattooed, but dressed appropriately, then no, that is wrong. If someone was attired correctly but had a hunchback and hairy moles and was just ugly, then it would be discrimination, and the owners would be wrong if the person met the dress code.
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