This is a piss-poor article that doesn't mention the crucial fact about this case, which is that nobody actually asked this person to create a same-sex wedding website. This entire proceeding was about a made-up hypothetical case, and I gather it's extremely unusual for SCOTUS to accept to hear something like this. Basically, the whole thing was engineered by "conservative" legal strategists because bona fide previous cases hadn't yielded quite the desired results (reasoning in the judgment too narrow for their purposes, etc.)
As an aside, and a long-time bug bear, it's also piss-poor journalism to use the euphemism "Christian" when what is meant is "right-wing evangelical" and excluding the actual majority of moderate, non-batshit members of mainline denominations. It's a colonialism use of language that sadly the US media have swallowed hook, line and sinker, but I'm really disappointed to see it used by a British site which probably cut and pasted the article wholesale.