Right. They might have wanted a cake with gay symbols on it. But Phillips made his mind when the couple said they wanted a wedding cake for their wedding. It wouldn’t have mattered if it’s a pride flag or an asteroid on the wedding cake.
Incorrect. The gay couple did not even detail the cake’s design. They said they wanted a cake for “our wedding,” and since Jack Phillips believed homosexuality was a sin, he thought providing any kind of wedding cake would violate his freedom of religion. He did tell them they could get other kinds of cakes, just not a wedding cake, and that includes plain wedding cakes.
Phillips even said, “I’ll make your birthday cakes, shower cakes, sell you cookies and brownies, I just don’t make cakes for same sex weddings.” (Notice the lack of nuance: he wouldn’t make any cake, whether it’s plain or designed.)
You can read more in the opinion of the Supreme Court [1], page 4 (7 on your document viewer).
P.S. A good argument can be made that the Colorado Commission didn’t violate religious neutrality. As Ginsburg outlined in her dissent, Phillips wouldn’t make a wedding cake for any gay couple. So there is a subset of people he discriminates against just because of who they are (gay couples), and another he doesn’t discriminate against. The other bakeries involved that rejected William Jack’s request to make cakes depicting homosexuality as a sin wouldn’t make such a cake for anybody.
To make it easier to understand: Jack Phillips makes plain cakes he gives to one group of people but not another. On the other hand, the other bakeries wouldn’t even make a cake depicting homosexuality as a sin for anyone. So it wouldn’t matter if it’s an atheist or Christian or Muslim. Plus, the very same bakeries made cakes for other Christians and decorated beautiful Bibles, so it’s clear they didn’t find someone’s religion a reason to deny them a cake.
Phillip’s argument might be more convincing if he was asked to, say, design a wedding cake with a rainbow flag. But the gay couple were refused a plain, let alone designed, wedding cake.