IF you deny someone of your business because of a persons race, sex, or sexual orientation, THEN you'd be one of those things. IF you're ok with someone doing that, it makes you an ***.
I would not personally care to deny anyone access to my business based upon race, gender, or sexual preference.
However, I believe any person should have the freedom to decline business from any other person for any reason they wish - even the ones you mention here.
The reason is simple: No one should force you to do business with anyone, ever. You have a choice of who you want to do business with, and so does everyone else.
In your ice cream shop example, the customer can choose not to frequent that particular ice cream establishment - for any reason they want - and choose any number of other options instead. The could go to another ice cream shop. They can buy ice cream at the store and eat it at home. They can simply decide not to have ice cream that day.
By the same token, the ice cream shop owner can also refuse to serve ice cream to whomever they wish - for any reason they want - and choose to serve to other customers instead. They could even refuse to serve anyone and close early or shut down permanently if they want.
To make a law that says the ice cream shop must serve anyone who wants to be a customer is wrong, because it takes away the owners' freedom and makes the exchange unequal, and that isn't how a free market system works.