You didn't answer my question.
We know that the court doesn't agree with you when it comes to the issue of employees versus employers. That is, religious activity in the context of one's employment against the wishes of the employer isn't protected. And in this context, an employee of a company that makes these invitations or that bakes cakes can be fired (without recourse) for their discrimination if it runs contrary to the employers policies. This was reiterated as recently as this past Tuesday by SCOTUS in their decision not to accept the petition in Kennedy vs Bremerton School District (where the employee was fired from his coaching job for praying on the field following games). The distinction that is made is that employers cannot regulate private speech (as opposed to public speech) in contexts where free speech is an issue. And it could be debated (but not in this case) that an action is private as opposed to public.
And in connection with this, we know that the government can in fact compel speech (contrary to Provoman's assertion). While this is particularly true in the case of individuals who are employed as civil servants whose personal beliefs are largely irrelevant to the job they are required to perform, it is also true of corporations (who are regularly compelled to create speech). For example, the Surgeon General warnings on tobacco products are a recognized form of compelled speech. Teachers in particular, are considered by the courts as "speech for hire" which means that their students have considerably more free speech rights than they do within the formal context of their employment. This is well established in case law.
The issue though, is that in this distinction (which you seem to be failing to recognize) between speech and speech for hire, is that there is no assumption in speech for hire of the idea that the person who is creating that speech is demonstrating their own personal beliefs. When I worked for the Daily Herald many decades ago, I routinely produced advertisements for grocery stores. No one looks at a grocery store ad, and assumes from the images that are put there for the sale on beer, that the person making that ad is endorsing the consumption of alcohol. We all recognize that the ad reflects the intentions of the grocery store who purchased the advertising (to sell alcohol). Likewise, at a wedding (or even for the recipients of a wedding invitation), no one who gets one, or goes to the wedding, cares at all about any speech that might be coming from the artist who designs the cake, or the invitation. It isn't recognized by anyone else as speech on the part of the creator. It is a speech by the person who has purchased it. This is the issue with speech for hire.
We can see the normalcy in this, perhaps, from that well known painting that was requested by the LDS Church, where the Church required the artists to go back and remove all the angel wings. Was the Church refusing to let the artist's speech stand? Or was the painting really a speech act produced by the Church, employing the artist in the process? This is recognized in a number of court proceedings that are working their way through the appeals process.
The wedding cake case in Colorado simply avoided this question. SCOTUS made a very narrow ruling that had little to do with the question of what constituted speech. Telescope Media Group vs Kevin Lindsey (the Minnesota case with the wedding video producer) tackles this head on - since part of the original decision involved this specific issue. And this makes it much more likely to become an issue for SCOTUS should it decide to eventually take the case on appeal. The original decision clearly identified the video as speech-for-hire. Here are a few statements from the original District Court decision which is currently being appealed:
In the foot notes, the decision notes at this point that:
In other words, if the product is speech-for-hire, then the producer or the "conduit" cannot themselves claim that it is protected - that can only be done by the client who purchased it.
It is clear (at least to me) that the religious right is looking for a way to create a new application of free speech principles - not to to use an existing and long-standing principle to defend themselves. They want to create a new right to discriminate.
This question of speech-for-hire is absolutely essential. Because it becomes the core of this argument. Taken from a religious perspective, I know of no religion that makes it a sin to bake a cake for a gay wedding, or to produce a marriage invitation to a gay wedding. There is a certain amount of absurdity in the idea that somehow, this forces people to act in a way that is contrary to their religious beliefs.
And to carry this further, think of the implication of making videographers, and wedding invitations the speech of the artist. They then become liable for any suits arising from the message, and they release the client who purchased it from any liability rising from the message. That too is an absolute absurdity.
I expect that the courts will eventually define things like the cake, and the wedding invitation as speech for hire, and this will have an impact on the decision to define this as not protected.