Those who oppose gay marriage equality like to often use the scenario that you wouldn’t demand ham at a kosher deli to put across their point that businesses are free to refuse service to gay and lesbian customers. They claim that both scenarios are the same, so, why do we view the deli as acceptable but the refusal of a service to a gay wedding as discrimination. The reason why is we’re talking about services here, not particular products.
A person who opens a kosher deli is opening a business with the explicit intent of serving a product that is kosher. The deli owner is setting up to serve the needs and wants of a part of the population who observe kosher food preparation and consumption. They create their product to fit that need. Kosher delis also advertise that they are kosher; making it explicitly clear that you aren’t going to get your ham sandwich here.
Similarly, vegan bakeries are set up to serve a another specified product; one made sans animal products. They do this to for those for the specific part of the population who wishes their food to be made in this way. Vegan bakeries have set up to explicitly serve those customers and advertise as such. This is the reason why you would not be getting a ham and cheese croissant in those places.
In both of the above scenarios, each business would still be required to serve the non-vegan and non-kosher population. They may not have the particular product you want, but they would still be required to serve you from the selections of products they have.
Kosher observing or not, the kosher deli would be required to serve you. They don’t have to serve you ham, but they would have to serve you something from what they carry. They could not refuse to serve you because you are not kosher.
The vegan baker can’t refuse to cater the wedding of the non-vegans. They can refuse to make meat dishes because they specialize only in vegetarian fair, but they can’t just flat out refuse to cater at all. They still are required to provide their services within the parameters of what they offer as a product.
Baking a wedding cake, taking photographs and providing accommodations for a person to celebrate or sleep in are all services. As services, it is, also, required that they be available to all the public.
The Christian or Bible-believing baker is baking cakes. Baking is a service. There is nothing explicit and immutably heterosexual about baking that makes a cake a straight cake. There is nothing immutably heterosexual about a taking a photograph or operating a restaurant or a hotel. And as much as they want to believe it is, there is nothing explicit or immutably religious about any of those services either. Therefore, they are services that are available to all the public.
To put this in a bit of perspective in a reverse scenario. Gay bars are also set up to serve a particular part of the population. They serve the part of the population that is lesbian, gay, bisexual or transgender. Gay bars are in the public space, so, even though they cater to a certain population, they could not refuse to serve one of the many straight groups of bachelorettes and their parties that frequent gay bars. We couldn’t refuse them just because they are straight bachelorettes, because that would also be discrimination.