Businesses have the right to refuse service to any individual for any reason.

They do not have the right to refuse services to protected classes of individuals based on their belonging to that class when they provide those services to other equally qualified customers.

The first is about individuals. If a black gay female comes into my store, acts like a complete and total jerk I can toss them out for not being someone I want to do business with. I can refuse service because I don't want to be busy that day. I can refuse service because I don't like them individually. I can refuse service because I just feel like it.

The second is about groups of people. I can not refuse service to black gay females because they are black gay females. I can not withhold services from a person for reasons that have nothing to do with them individually and result only from my assumption of their inclusion in a particular group.

The reason for this is simple but multi-faceted and rests on a few bits of reality that people don't like to think about sometimes:

1) Businesses exist because of civil society. There's a reason Somalia isn't a libertarian utopia even though there's absolutely no government interference in business. It is because there is no civil society at all that businesses can not function there at all. This is more than just about government and law enforcement too. Governments allow the existence of a high functioning civil society: working infrastructure for business; schooling so that businesses have literate employees; working financial systems by which to transact business; means for customers to move from business to business safely to conduct transactions; and so forth. However, governments are not the sum total of a high functioning civil society. This requires more than a government. Syria has a government. But the people of Syria are not free to live their lives unencumbered by unnecessary interferences in their lives. The question is what interferences are necessary and which are not. Civil society, in the experience of history, seems to work best when all members of society can decide that question together; and with their collective, rather than individual, best interests as the focus.

2) Because business depend on civil society, civil society has authority to tell businesses what they can and can not do in order to maintain that civil society. This includes following laws that limit the freedoms of businesses. Businesses, just like individuals, have to respect the rights of others. You can not intentionally harm other people for no justifiable reason. While you can punch someone in self-defense, the legal defense against that charge is a positive defense not a negative one. That is, you can't say "self defense" and walk away. You generally have to be able to show that it was self-defense. You can punch someone in the face. But if you don't have a reason for doing so that society accepts as valid, you've violated their rights and exceeded your own. Likewise, businesses can't do things that are obviously harmful to society, such as dumping raw sewage into the public drinking water.

3) One of the lessons of the civil rights movement is that "separate isn't equal." For civil society to work we all need to have reasonable access to the aspects of society that make society function as a civil society. It is a violation of an individual's rights to execute their own life to preclude them from society on the basis of basic discriminatory practices of the majority. We can't simply say we don't want black people in our schools, or that gay people can not drive on the roads, or that women shall not have access to jobs. And again, we know that civil society is more than merely the collection of government functions. It doesn't matter if black people have access to the same rights as white people if there are no black people in the area because no one will do business with them outside of the government.

4) Civil society, while dependent upon government is more than government. Through the 1900s people exercised their "individual freedom" to refuse business to those in minority groups. The results were segregated communities where black people simply could not live. No one would sell them a private home because the mortgage clauses came with rules against reselling the homes to black people. No one would sell them food, because the local grocers wouldn't do business with "those people." No one would treat them if they were sick and injured, so they would die without proper medical care unnecessarily. None of this involved the power of the state. But the collective actions of individuals of the majority precluding minorities from participating in civil society created significant civil strife and endangered civil society's continued existence.

5) Ergo, the people of the democratic republic demanded that civil society address the issues of lack of inclusion of minorities. The result was that civil society decided collectively that businesses were free to exist and operate within civil society but one of the personal rights they could not violate was the right to not be discriminated against based on membership in a protected minority. Now, this law has plenty of controversy around what should and should not be a protected minority. However, there's absolutely zero basis for any contention that civil society, upon which a businesses ability to exist depends, lacks the authority to set such rules. Further, the experience of the nineteenth and twentieth centuries demonstrates quite clearly that failure to consider overt discrimination a crime resulted in significant social harms that negatively impacted civil society in a way that was considered unacceptable, and legitimately threatened it's continued existence.