WASHINGTON — It all began with a cake, but now businesses across the wedding industry are closely watching what happens when the U.S. Supreme Court convenes Tuesday to hear the case of a religious Colorado baker who refused to do work for a gay couple who were getting married. At issue is whether Jack Phillips, owner of Masterpiece Cakeshop in Lakewood, had the legal right to turn away fiancés Charlie Craig and David Mullins when they asked him to bake a wedding cake in 2012. Phillips contends his cakes are art and that doing so would violate his Christian values and right to free expression; Craig and Mullins counter that it’s discriminatory to refuse them a service offered to other customers. Ruling could sway a vast industry While the case has the potential to affect a wide range of businesses, attorneys on both sides agree the ones most likely to see an impact are the florists, photographers and others who make up a U.S. wedding industry that accounts for tens of billions of dollars a year. Supporters of Phillips argue that if he loses his legal fight that like-minded entrepreneurs with a religious objection to same-sex marriage effectively would be barred from doing wedding work. A loss would “provide a road map for litigation against Christian photographers who are bound by religious conviction not to offer their artistic talents to photograph a same-sex wedding ceremony or celebration,” wrote the International Christian Photographers in a brief filed to the high court. Attorneys aligned ideologically with Craig and Mullins paint a different picture: A ruling in favor of Masterpiece Cakeshop would open the door for widespread discrimination — starting with weddings and spiraling outward. “It is not hard to imagine the claims that will follow this case: A jeweler may argue that his religion forbids him from selling wedding rings to an interfaith couple; a shop owner may refuse service to women customers to avoid contact prohibited by his religion,” wrote attorneys for the Denver Metro Chamber of Commerce and more than two dozen businesses. Attitudes have changed since same-sex marriage legalized The dueling arguments are what one wedding professional