My reading of the whole decision was "You can deny people their First Amendment rights, but you have to be nice and polite while you do it", and it was tailored that way to get Kagan and Breyer to go along with it. If you look at what she said in that light, you'll see that's EXACTLY what she's saying. The decision doesn't actually give any protection to First Amendment rights, OR the ability to act on your beliefs or conscience; it simply insists that the bureaucrats have to pretend to respect your rights while they deny them.
Then what was all that wording in the Opinion about how a man of faith cannot be punished for practicing that faith at all times, even in the marketplace?
Really? You thought the Court said that governments only have to pretend to respect people of faith's 1st Amendment protections while they can simultaneously deny them?

Yer funny.
Well, let's look at it.
"While it is unexceptional that Colorado law can protect gay persons in acquiring products and services on the same terms and conditions as are offered to other members of the public, the law must be applied in a manner that is neutral toward religion. To Phillips, his claim that using his artistic skills to make an expressive statement, a wedding endorsement in his own voice and of his own creation, has a significant First Amendment speech component and implicates his deep and sincere religious beliefs.
His dilemma was understandable in 2012, which was before Colorado recognized the validity of gay marriages performed in the State and before this Court issued United States v. Windsor, 570 U. S. 744, or Obergefell. Given the State’s position at the time, there is some force to Phillips’ argument that he was not unreasonable in deeming his decision lawful."
In other words, it may have been arguable that it was okay - not that it WAS okay, just arguable - when he did it, because same-sex marriage hadn't yet been legally recognized, but NOW it wouldn't be, because NOW his Constitutional rights have been superseded by Colorado law.
"Phillips too
was entitled to a neutral and respectful consideration of his claims in all the circumstances of the case.
That consideration was compromised, however, by the Commission’s treatment of Phillips’ case, which showed elements of a clear and impermissible hostility toward the sincere religious beliefs motivating his objection. As the record shows, some of the commissioners at the Commission’s formal, public hearings endorsed the view that religious beliefs cannot legitimately be carried into the public sphere or commercial domain, disparaged Phillips’ faith as despicable and characterized it as merely rhetorical, and compared his invocation of his sincerely held religious beliefs to defenses of slavery and the Holocaust. No commissioners objected to the comments. Nor were they mentioned in the later state-court ruling or disavowed in the briefs filed here.
The comments thus cast doubt on the fairness and impartiality of the Commission’s adjudication of Phillips’ case. Another indication of hostility is the different treatment of Phillips’ case and the cases of other bakers with objections to anti-gay messages who prevailed before the Commission. The Commission ruled against Phillips in part on the theory that any message on the requested wedding cake would be attributed to the customer, not to the baker. Yet the Division did not address this point in any of the cases involving requests for cakes depicting anti-gay marriage symbolism. The Division also considered that each bakery was willing to sell other products to the prospective customers, but the Commission found Phillips’ willingness to do the same irrelevant.
The State Court of Appeals’ brief discussion of this disparity of treatment does not answer Phillips’ concern that the State’s practice was to disfavor the religious basis of his objection."
So it appears that their objection is not to the decision, but the way the case was conducted, and the way the decision was reached. In other words, they're not saying that Colorado was wrong to deny him his rights, but that they didn't deny them in the right way.
"In view of these factors, the record here demonstrates that the
Commission’s consideration of Phillips’ case was neither tolerant nor respectful of his religious beliefs. The Commission gave “every appearance,” id., at 545, of adjudicating his religious objection based on a negative normative “evaluation of the particular justification” for his objection and the religious grounds for it, id., at 537, but government has no role in expressing or even suggesting whether the religious ground for Phillips’ conscience-based objection is legitimate or illegitimate.
The inference here is thus that Phillips’ religious objection was not considered with the neutrality required by the Free Exercise Clause.
Once again, we are not hearing "The Free Exercise Clause guarantees his right to refuse", but only that it guarantees that the government will act nicely when deciding whether or not he has rights.
"Whatever the confluence of speech and free exercise principles might be in some cases, the Colorado Civil Rights Commission’s consideration of this case was inconsistent with the State’s obligation of religious neutrality."
Hey, look. Confirmation that they are NOT deciding whether or not the First Amendment trumps Colorado civil rights law, but only deciding on whether the Commission approached the question with the right attitude.
"Still, the delicate question of when the free exercise of his religion must yield to an otherwise valid exercise of state power
needed to be determined in an adjudication in which religious hostility on the part of the State itself would not be a factor in the balance the State sought to reach.
That requirement, however, was not met here."
Once again, "we're not saying whether the decision was right or wrong, only that you didn't go about it correctly".