Same-sex civil marriage has become legal in various jurisdictions and states. What should those do who do not recognize the moral validity of these marriages? This has become an issue for people personally and in business.
Consider the latter first. There have been cases of a photographer and a baker: what should they do if customers ask for a cake or photographic services for a same-sex wedding? This is not a case about the customers themselves but about the use or customization of a product or service.
In general what a customer does with a product or service is their business, as long as a criminal enterprise isn’t involved. Other objectionable uses are possible, too. Custom T-shirt providers should be free to reject objectionable messages. But a baker should not object to making a standard wedding cake for a customer who uses it as they desire.
Wedding cakes often carry ornaments on top depicting a bride and groom. What if the customer requests an ornament with two grooms or two brides? If the bakery does not have such ornaments, they simply say so. It’s not a product they sell.
Services such as photography are customized to some extent so how they are advertised makes a difference. Until now, advertising “wedding photography” was pretty well understood. The term covers marriage ceremonies in general. If there are particular aspects of an ethnic or religious wedding that the photographer is unfamiliar with, then either the customer hires a different photographer or negotiates their specific requirements.
Photographers who don’t want to photograph same-sex weddings should imply that in their advertising. “Traditional wedding photography” would tell customers what services the photographer offers. Customers should not expect other services. It’s possible the courts won’t accept that, but it remains to be seen how else they will set the boundaries of what can and can’t be done.
An example of a personal issue would be an invitation to a same-sex wedding ceremony from a relative. There may not be one answer for everyone. On the one hand, God “makes his sun rise on the evil and on the good, and sends rain on the just and on the unjust.” [Mt 5:45] On the other hand: “Bad company ruins good morals.” [1 Cor 15:33] “Take no part in the unfruitful works of darkness, but instead expose them.” [Eph 5:11]
The best policy is to have a policy and stick with it. Then people know where you’re coming from and aren’t arbitrarily picking on them. And be able to defend your policy.