"Don't try to church it up." (Bill Wetzel) This advice comes from a Blackfeet wise man, so all the liberal whites out there -- the ones that remember what a church is -- should take it seriously.
In human behavior (at some kind of norm) the sense of virtue (what is right and what will get you at least yelled at) is something that begins to develop as soon as a child is born. After parents and then expanding to the family consensus, there are generally two sources of learning. One is institutions and one is stories. Beyond that, two institutions strive to instil a sense of what is right or wrong: one is the church and one is the state. They are constantly trying to reconcile or enlist each other through stories and laws. (More recently, the laws have been enforced with physical punishment, including death, because this essay is about the world -- not just the US.)
Sometimes the law (criminalization) is in league with religion, which means that both must be defined and consistent -- more or less. A baker refused to bake a wedding cake because of not believing in same-sex marriage -- even if the cake is not topped by two grooms or two brides, even if someone at the reception adds them to the cake. Even if they will benefit greatly from the ensuing publicity and the satisfaction of righteousness. Even if a wedding cake is a social convention and not specifically "religious" as it would be if it were a communion wafer.
If a bakery refuses to create cakes for gays, that creates an opening for a bakery that will specialize in such an enterprise: gay cakes. For a while there was a craze for wedding cakes and other event cakes or even non-event cakes that were obscene. This is also a social convention. There is no religious law that specifically forbids a cake to be frosted with imitations of human genitalia. Anyway, the idea that only religion can permit conjugation -- that is, one can only have sex if married -- is pretty much blown out of the water. It was enforced by conception -- real consequences. Once that was gone, the religious and governmental guides collapsed.
Gay and lesbian behavior or beliefs or desires were enforced by economic consequences. The Christian arrangement was that every woman was owned and fed by her husband. Once a woman could make her own living, at least in this country, there was no need to require every man to "keep" a woman or every woman to be "kept" by her husband. This upset the order of society so deeply that the incel fellows were desperately offended, but they declined to move to a country where they could buy a wife and beat or rape her however they wanted. (Maybe they realized that if they did, they'd still be losers and they'd have to pay her bills.)
Why would a same sex couple want to ape heterosexual marriage? What is marriage? There are competing points of view that define the government/religion schism. For the government, it is necessary to keep track of ownership, transactions, legal status, and -- crucially -- who can be held responsible for economics and criminal behavior. As soon as writing was invented, the tally began. As soon as the Rule of Law was established, which was pretty long ago because it was linked to the establishment and power of religious institutions to link to conception, birth, marriage, divorce, death, and privileged categories like priests. Their ploy was to enlist God as their judge and punisher.
The government built on that, using the idea of "sacredness" to fortify their own power of courts and armies (civilly called police). In the end cakes and other social symbols like white dresses or the groom's "last" night as a bachelor -- which were about sex -- were irrelevant. They have not been criminalized. Judges can not care whether a cake broke Biblical rules -- there aren't any about fancy cake -- so they pretend the offence is about freedom of religion.
If a baker knew that people were committing bigamy, could he refuse to bake a cake with two brides, two grooms? If he knew that either of the parties were unfaithful or that the relationship had been out-of-wedlock and even produced children, could the baker refuse to tell them a cake? A priest or minister could refuse to marry them. Although I got into trouble as an intern when I refused to marry two youngsters because the male had covered the female with bruises. I was considered prejudiced and the marriage was defined as redemption. The state had no problem since the marriage license was only used to establish age, disease, and the legal moment of status change. How do Mormons manage polygamy?
Would a baker create a cake celebrating "cross-species" fealty -- putting a person and a German shepherd on top? Some would. Why tell a baker what the marriage actually entails anyway? Why does a cake have to be topped with the entities involved? Why have a cake in the first place? The government doesn't dictate what the ceremony has to be like or whether there is any ceremony at all, except the signing of documents to make the record.
In some denominations the center of power and authority is in the congregation rather than the clergy (a democratic idea) so it is the congregation that signs the document, one might say "a cloud of witnesses." A rather nice symbolic cake might show a circle of people rather than the marrying couple. It would be a nice touch if they were dancing.
The religious control of marriage in this country is pretty much ignored. The governmental control of marriage is incomplete, blind to nondocumented sexual cohabitation of whatever genders, and unable to draw a clear line between marriage and ownership, such as pimping.
But the sacredness of honorable intimacy is so central and vital that it may even be expressed molecularly as found in the studies of wild rodents and probably other life forms. Why not have swans on top of wedding cakes? Ooops. In England swans are emblems of death because they are so serene on top and so busy under the water. So much of our lives are like that.