I agree that a business should not have to accommodate the abomination called same-sex marriage, but Chick-fil-a's not going to have a litmus test to buy a sandwich. Then again, if they wanted to, that is their prerogative.
You are exactly right. A business relationship is generally simply an economic one and both parties choose to put almost all differences they may have with each other aside in order to mutually benefit. However, some types of business requires a level of personal involvement and different people are willing to allow only a certain level of that before some differences can become material.
For example, if I owned an electric utility, how could it be any of my concern what people did with the power they were using? But since I know what God thinks of two people of the same sex attempting to “marry” (which for them is physiologically impossible) I cannot in any way allow my creative talents to be hired to help them conduct that ceremony.