So what is the difference? The baker isn't refusing his normal products or services to anybody. In the most notorious case, the baker had been selling baked good to the gay couple for some time, knowing they were gay. And he didn't refuse to bake a cake for them because they were gay. He refused to participate in a gay wedding that he could not condone. It is the difference between discriminating against somebody because of who they are and choosing what activities or events we will condone.
I have no problem seeing that difference. I don't know why it seems so difficult for so many to grasp, or maybe most just pretend they don't see it so they will be justified in punishing Christian values they disapprove of?
The most notorious baker (what a turn of phrase

) was never asked to participate in the wedding in question. They were no asked to cater the event, to cut the cake, or even to wear the appropriate attire of guests or workers of the caterer.
So the question really is, how would they have been attending and in what role?
They would have had to deliver the cake to the event and almost certainly would have had to do some assembly and final finishing touches at the event. And their truck would be parked outside the event advertising that they were party to the event. Nobody should be forced to do that for an event they believe to be wrong, immoral, unethical, etc. The Christian bakers should not be forced to do that. The gay baker should not be forced to provide a special product or service for a Westboro Baptist event. The black baker should not be forced to provide a special product or service for a KKK event. Etc. Participation or contribution for an event is a very different thing than selling products or services you normally have for sale.
"Party to the event?" You equate a gay baker being offended by Westboro Church with Christians offended by gays getting married? The Christian Westboro people hate and condemn the gay baker. They would assault the baker's very being and personhood. What equivalent offense would the other Christian have with the gay couple?
"Participation or contribution for an event is a very different thing than selling products or services you normally have for sale." - your words.
No one should "be forced to provide a special product or service" - again, your words
A baker decorates a cake. A baker puts specialized decorations on every single wedding cake, unless one wants one without the decoration. Wedding cakes are special products.
Delivering a cake to the wedding of a gay couple could never be construed as being a 'special' service.
You keep defending the so-called right of any person of faith to deny products or services to the wedding of a gay coupe just because they claim to believe weddings of gay couples to be wrong, immoral, unethical, etc. Without a legal justification of this type of discrimination in the public square you'd be supporting anarchy.
Any claim of supporting 'liberty' is always a hard sell. Your arguments so far have failed to provide a defense of any 'liberty', and just using the term liberty without defining the specific liberty in question is an exercise in futility.