I don't think any rational person assumes
I disagree. I think that some rational persons, in particular many religious persons, consider themselves accountable to God for all symbolic activity in which they engage.
This view is supported in the New Testament in 2 Corinthians 5:20, which calls Christians to be ambassadors for Christ. Engaging in a form of symbolism is an act of speech.
The Old Testament / Hebrew bible is full of strictures against engaging in symbolic support of claims that the Lord is not in charge of everything and worthy of exclusive worship.
Thought experiments involving role-reversal are useful for everyone in this kind of discussion. Would you consider it okay for the law to compel a Muslim-owned advertising company to write "Islam is wrong. Mohamed was a militant con artist" all over a city's billboards? If not, why not?
Or would be okay, on your view, to force a Jewish-owned movie-making company to produce and promote a movie claiming that the Jews had it coming in the Holocaust, if it could somehow be shown in court that the submitted script was a guaranteed money-maker for them?
My contention is that some Christians consider writing messages counter to their theology to be objectionable in the same way. And that the very debate about whether or not it's sufficiently a matter of compelled religious speech is itself a question whose answer depends on one's religious viewpoint.