To to respect an individual’s autonomy is to allow an individual to develop opinions, make choices, and act as they please, unless their actions are clearly detrimental to others. Refusing to serve you, the customer, is not detrimental to you. Also, forcing business owners to serve customers they don't want to is detrimental to the human respect we should have for each other.

Firstly, it is not detrimental to customers if a business does not want to serve them. This is because if a business openly declares itself as discriminatory, those discriminated against and their allies can readily give patronage to businesses that approve of them. In this way, we punish behaviors we disagree with and reward behaviors we agree with. If businesses were not penalized for being honest, customers would be able to make more educated decisions.

Secondly, it is detrimental to the business owner's autonomy to force them to do business against their will. They became entrepreneurs because they want to be their own boss, but when the government forces people to associate with each other, they have become servants of the state. In my own house, I can choose to kick anyone out for any reason, and that is just. Why is it any different when the place is a privately owned business? The owner pays rent and utilities. They should be able to set the rules, because they own the place, just as you own your home.

I would like to make a distinction here, because my opponents might tell us that sometimes the government is right to make us do things for the greater good, but that would be a subtle lie. The government is sometimes right to tell us what NOT to do (i.e. laws against murder) to keep us from an action, but the government is wrong to make us perform an action, (i.e. You shall live in Wisconsin, you shall buy broccoli, you shall hire this man), the exception being taxes.

Thirdly, if everyone was forced to do business with people they didn't want to, the customers would have to abide by the same rules. Imagine if the roles were reversed..."You didn't come to my business because we're Muslim owners. You must receive a punishment." Choice would become obsolete. There would be no such thing as choice. Such a world could only exist if there was a higher power, in which case our topic of autonomy is meaningless.

Finally, businesses usually have good intentions if they turn a customer away. They are appealing to a certain demographic and trying to make that demographic feel at home, much as a fancy diner turns customers without shirts away to put the targeted customers at ease. Appeasing one customer could very well upset another, but trying to appease any is at least a sign of good intentions. Furthermore, if their intent is to be honest with customers, that is ethical. Moreover, let's say a religious business owner does not want to sell a cake to gay couple for their wedding. This person may believe being gay is a sin, and therefore to help a gay wedding is akin to giving alcohol to an alcoholic. In this hypothetical, their intentions are good, because they want to help a sinner. You may not agree with his/her logic, but if you respect free speech, you have to allow him/her to disagree with you.