Where does obligation lie?

Let's play Imagine That. It won't hurt.

Let's imagine a Mike and Jenny Smith. They're committed vegetarians. They walk the walk, talk the talk, but aren't out to convert anyone. They just want to help others by encouraging them to lead a healthy lifestyle, providing them with both an opportunity and an example. What they do is open a vegetarian restaurant. What would they call it? Let's say Meet Without Meat. Play along with me, what would their logo be? A cow, pig and chicken all sitting around a table?

Now, it's a good restaurant. The food is flavorful and generous, the kitchen clean, the service courteous. It becomes a popular restaurant even among non-vegetarians. Catholics like it to observe their Friday abstention, Jews like it because it's effortlessly kosher, Muslims like it because they don't have to worry about the pork, Hindus like it because of the no-beef thing. Some folks even visit occasionally just for variety. Everyone is happy, Mike and Jenny are doing well. They do so well that they open other locations, thus becoming a chain.
Now, nobody is forced to patronize their restaurant. Everyone who walks through the door knows it's a vegetarian restaurant; it's not a secret. It's obvious by the name and the logo. As we imagined, some choose Meet Without Meat because they know it's vegetarian. Can you picture it?

Now let's imagine some human toothache coming through the door, being seated, and ordering.... a hamburger.
How politely would the server have to inform this customer that item isn't served there? If the customer proceeded to insist, would the proprietor of the restaurant be out of bounds to step in and invite said customer to choose another establishment for his dining experience? Should Mike Smith have to volunteer the names of his meat-serving competitors, provide a local restaurant guide or phone book, or just have the bum escorted to the door? Would it not be madness to suggest that Mike is obligated to provide transportation to Toothache's new destination? And who in their right mind would say the customer has the right to sue Meet Without Meat for not providing him with his meal of choice--a choice they find morally reprehensible?

I wonder.