If _the government_ stopped them from doing anything of the above, that would be a free speech hinderence. Now it's just business.
Amazon has not violated the first amendment, but they have violated free speech. It is not illegal to do so, but people often agree and disagree with actions on bases other than legality.
Do you think the bakers should have been forced to bake the gay couple a cake?
If we are talking about pretty generic wedding cakes, where say the baker just bakes N cylindrical cakes of decreasing radius, stacks them coaxially, covers them in icing, writes the couple's first names on top, adds a few frilly but pretty standard decorations, and shoves a couple little plastic figures on top to represent the couple, and the only thing that makes it a "gay" wedding cake is writing two male names or two female names instead of one of each, and shoving in two male or two female figures instead of one of each, then yes, the baker should have to serve gay couples.
If we are talking about the kind of wedding cake that you'd get by going to a place like Charm City Cakes in Baltimore (the cake shop that was the subject of Food Network's "Ace of Cakes" series) and asking for a custom cake, where you are hiring an artist whose medium happens to be cakes, who is going to make you a unique cake where the artist is going to express their own artistic vision and interpretation of the your marriage, where the cake is very much an act of speech by the artist, then I don't think the baker should have to serve gay couples. These cakes are necessarily acts of original speech by the artist, and that should not be forced (even if the person who wants the cake is in a protected class)--the artist should be free to only create works where the artist's feelings match what the buyer wants.
Christian book stores can't exclude Hindus from buying their books. One upon a time they could, but that's now illegal.
There is no law saying Christian book stores must stock the Bhagavad Gita.
There's also no law saying Amazon must stock certain books. But there are laws preventing Amazon from excluding certain classes of people as clients.
To your question, the Supreme Court has said that lack of religious neutrality by the Colorado Civil Rights Commission was inappropriate, in such a way that the case should be overturned.
I'm pretty sure I did know that as checked the Supreme Court decision while working on my comment, and it says https://www.supremecourt.gov/opinions/17pdf/16-111_j4el.pdf
> Masterpiece Cakeshop, Ltd., is a Colorado bakery owned and operated by Jack Phillips, an expert baker and devout Christian. In 2012 he told a same-sex couple that he would not create a cake for their wedding celebration because of his religious opposition to same-sex marriages—marriages that Colorado did not then recognize—but that he would sell them other baked goods, e.g., birthday cakes.
In my comment I removed text where I quoted from the decision, as there's no way that decision can be discussed in the sort of off-handed way that jpxw brought it up.
Also, I didn't realize there were multiple relevant cake maker lawsuits, so perhaps jpxw could be more specific, as the Supreme Court decision doesn't seems to have a direct bearing on the topic, leaving the underlying issue in confusion.