The baker in your chosen example is very convenient in that they are clearly anti-gay. Consider the the real life examples of bakers who are allegedly happy to serve gay couples, but believe that baking a cake for a gay couple's wedding would be a speech act in which they do not wish to engage, or a hotel providing 'separate but equal' treatment to people of colour. These things strike me as problematic, but clearly were not obviously so to the legal system of the time.

I think you're likely to run into the general issue that people seldom phrase their motives so as to make themselves sound unreasonable or intolerant.