The problem in total reduces to:
The owner of the business, cake shop, is wrong since he denied service to someone based on his prejudice, which in his case MIGHT be based on religion.
He broke the law.
Overall his business and all others must be apart from religion, this is what the law requires, and in that he needs to leave his faith at home while at work.
The only exception to that is if he claims he is a Church and he is a Pastor.
This is cake.
Not religion.
He has no right to break the law.
He has no protection under the law based on freedom of religion since we have a right to be free from his.
This IS WHY this bifurcation is in place.
What if this person sold you a car and refused to fix it since he learned now you are gay?
An ambulance driver?
A doctor?