The issue being whether "applying Colorado's public accommodations law to compel the petitioner to create expression that violates his sincerely held religious beliefs about marriage violates the free speech or free exercise clauses of the First Amendment."
With persistent rumors of the pending retirement of 81-year old justice Anthony Kennedy, there's speculation he is waiting to weigh in on this case before calling it a career. Why this particular hearing? David French at National Review speculates along the same lines as I do.
(I)f Justice Kennedy views this case primarily through the LGBT lens, then the First Amendment may well lose. Kennedy is obviously proud of his long line of LGBT-friendly precedents, and that pride has even led him to a relatively rare First Amendment misstep, so it will be critical to explain to him (and the other justices, of course) that this isn’t a case about “discrimination” but rather about forced speech. Framing matters, and the other side will wrongly frame the case as raising the specter of Jim Crow. The right framing is found in the First Amendment.
I specifically recall certain excerpts of Kennedy's majority opinion in Obergfell, which was the case that made gay marriage the law of the land nearly two years ago. It may be a glimpse into how he'll rule in Masterpiece, which is of particular interest given Kennedy may well be the "swing vote" on the 9-judge SCOTUS panel.
Many who deem same-sex marriage to be wrong reach that conclusion based on decent and honorable religious or philosophical premises, and neither they nor their beliefs are disparaged here. But when that sincere, personal opposition becomes enacted law and public policy, the necessary consequence is to put the imprimatur of the State itself on an exclusion that soon demeans or stigmatizes those whose own liberty is then denied.
As French noted earlier, it will all come down to how this case is presented. This isn't about denying people services due to their sexual orientation, which is illegal based on public accommodations laws. It's about one being forced to violate one's deeply held religious beliefs. In fact, I daresay that if a gay man walked into Masterpiece and informed Mr. Phillips that he'd like to purchase wedding catering services for his adopted son and the son's wife-to-be, there would be zero issue.
If precedence means anything here, let's just say I'm not terribly optimistic that Kennedy will err on the side of religious liberty in this case.