Obviously the people who own this shop are fundamentalist Protestants, which means that they will oppose a whole lot of things, not just homosexuality. But how do they know what their customers get up to? They'd think I'm a damned idolater if they knew my religion, but they'd serve me because they wouldn't know. For all they know they may be serving the local Satanist. If you run a business, you have to take your customers as they come.
On a more philosophic level, humans are social animals and a good human is one who acts in a social manner. The only fellow-members of society we have a right to object to are law-breakers. In private, we can draw our friends from those who are like-minded, but in public we own a duty of civility to our fellow citizens.