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Does the baker have any role to play in the religious ceremony? Do they have to sign off on the marriage? Or do they have to supply a good at a set price for the purposes of consumption? It doesn't matter what you "feel," it's a business transaction with no judgement on the actual ceremony.
The same argument could be made regarding the location. After all, people can get married anywhere and someone is just "renting" the facility. Therefore, any church that marries non-members on the grounds must marry anyone that asks. Under your standard only 3 people "participate" in the wedding: the two (for now) people getting married and the person performing the ceremony.
To be ridiculous about it, you could use the scenario of catering a Voodoo animal sacrifice. You're not actually participating by providing food for the occasion, and it is legal to slaughter your own animals. Should a caterer be allowed to refuse to cater for an animal sacrifice ritual if it violates their religious beliefs? Under your defnitions, they wouldn't be allowed to refuse.
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