The wedding does not occur in the place of business. If you ask a restaurant to cater your wedding, then they have to be present at said wedding. You cannot force a religious person to participate in an event which offends their beliefs, and it's pretty intolerant to expect them to.
It isn't about business. It's about individual freedom. In case you hadn't noticed, all businesses are owned, and operated by, individuals. Individuals should not be subjected to performing tasks which offend their deeply help beliefs.
If marriage is only about being legally bound, then go to the courthouse, get married, and be done with it. While you're at it, don't go to a religious shop owner and ask them to cater your reception.
How do you not see how this protects people who want to practice religion? If someone asks you to do something that violates your religion, you can refuse to do that thing, and be protected against litigation!
Where is it written that the state must separate itself from the church? That isn't even a law. That isn't even in the US Constitution. Also, for the record, the "separation of church and state" is meant to prevent the establishment of a state religion, like the Church of England. It is meant to keep the state out of religion, not to keep religion out of the state.