Pretty clear you are working with a definition of "religion" that necessarily invokes organizational, legally-established status.
I think the rhetoric OB and other progressives use is pretty tightly engineered to discredit personal convictions invoking God in any way, replacing them with legal technicalities which in effect make even personal beliefs legally prosecutable. It is really intolerance of religious conscience in individuals. People who reject statist rules are the problem. They are systematically reduced by law to criminal status.
OB might not have that intent, and might actually believe he is advocating a reasoned sort of society operating on better principles, but I am looking at what the net effect long-term will be if we have governments prosecuting individuals or business owners for not performing services they may deem objectionable on the level of their own personal conscience.
We have civil alternatives. . . . publicly-paid judges of various descriptions, widely available in all legal jurisdictions, who will perform legal weddings. The government does not need to regulate individuals on their own enterprise of serving any category of clientele in this manner. Nobody should have to do things they consider wrong. We even let some men called up for military service make a statement of conscientious objection so they won't need to kill people. Or at least we should, if we don't do this anymore.