Phillips is going to lose, I predict. I thought so from the moment the SCOTUS agreed to take the case. The SCOTUS doesn't, contrary to popular opinion, like to go out on a limb on issues of great public debate. The legal principle was established back in the sixties when the courts threw out the claim of a lunch counter owner that he could refuse to serve blacks on grounds of religion. Remember too that Phillips rejected the gay couple's business without first inquiring about the custom cake they wanted. Those are bad facts for the argument that different rules should apply to him as an "artist".
If you run a public accommodation, then the law requires you to provide the services you've advertised. The concept is simple, and fair.
What will happen, I think, is that the SCOTUS will rule against Phillips so the matter can be resolved through the legislative process. The right to be served in a public establishment without discrimination is a creature of legislation, and can be fixed (if the public demands) by legislation.