I support freedom and liberty no matter what! Equal rights for all.
If you truly believe in freedom, then anyone who doesn't want to rent to, hire, or do business with a Black, Gay, Jew, Muslim, Asian, White, Woman, or Man etc. should have such a right, no?
No, that's a bad argument.
Equal rights doesn't mean everyone gets to do exactly what they want. You don't have the right to murder someone.
Also, equal rights when you run a business becomes something different, you sign a contract with the society about how to run that business. Everyone has the equal right to start a business, but you have to agree to those rules first.
Also, right are basically you can do anything as long as it doesn't hurt or harm others. By having a society where groups of people are denied their place as an equal member of society, ie, by preventing them going into shops to buy stuff, then you are going against the theory of rights.