I believe you are making the same mistake the courts have, by confusing the PERSON making the request with the REQUEST being made.
I agree that a public business should not refuse service to a person for what they are. If a bakery sells wedding cakes, they should sell wedding cakes to everybody.
But a bakery should be allowed to refuse to sell a cake with a specific message, or with specific characteristics. For example, they should be allowed to not put to male figures on the top, or to write a pro-gay message on the cake. Messaging is a first amendment issue.
To the degree a person performs an act of artistic expressions, they should be allowed to dictate that expression. So, for example, a photographer should be allowed to refuse to photograph a gay wedding, but NOT to refuse to photograph a gay person.
In a really free society, a person should be able to serve whatever product they want to whomever they want, and not provide that service to anyone they choose.
Doesn’t mean there won’t be consequences to those choices (boycotts, pickets, etc.), but having the government force its choices at the point of a gun is the wrong answer. If the government selects your choices today, a new government can use that same power to select different choices tomorrow - sound familiar?