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The hard question presented by the case was this: did Colorado's anti-discrimination law violate the baker's First Amendment rights, to the extent it compelled him to create a cake for a same-sex wedding?
The Supreme Court sided, 7-2, with the baker. But the Court did so on much narrower grounds than the baker, and advocates, hoped for. The Court DID NOT resolve the conflict between religious belief and anti-discrimination law. In fact, the Court expressly declined to resolve that. Instead, the Court found that the question has to be resolved through a process free of religious bias and animus violating the First Amendment, and that here the Colorado administrative procedure showed clear bias.
Put another way, the Court said "however the question comes out, the decision-makers can't get there through express hostility to religious beliefs." The Court found that the Colorado administrative process showed just that anti-religious bias. There's an array of concurring and dissenting opinions that don't change the result, but that's the core opinion of the Court. So: the tension between anti-discrimination and the First Amendment is left for another day ... but Civil Rights Commissions can't indulge in gratuitous anti-religious rhetoric in the process of weighing such claims.
So they did not rule that the baker had the right to discriminate, they ruled that the case was tarnished. Expect to see another case like this rise through the courts again.