Firing an employee (assuming a private employer) based on race is not a government action either, and is certainly illegal. So your GOVERNMENT ACTION statement holds no water.
I did forget that the baker won in the US Supreme Court (at a cost of hundreds of thousands of dollars, and horrible losses due to bad PR as you pointed out) but that case only involved the message on the cake, not refusing to serve a gay couple. So as far as that goes, it was an inaccurate analogy on my part. If he had refused to serve them at all, it’s a slam dunk loser for the baker.