Laws never said anything about what you stop saying, in this context.
See: Apple vs FBI in San Bernardino.
It is important to note that the more "low-effort" style of warrant canary, or simply posting a static page that says that you have not been served a warrant, is probably not safe. Taking the page down is possibly an action you can be legally prevented from doing. However, that's not what rsync.net is doing. They are specifically posting a new one every week, because no court or authority can compel them to post one if they don't want to under US law.
Edit: My point is that "compelled speech" isn't the issue, it's "compelled false speech" vs "compelled silence", either of which infringes on the right to free speech in some way.
(That's not to say this argument, or any canary argument, would avail; who the hell knows, should be our watchwords in this matter.)
The FDA can't compel you to say anything you don't want to. But they can refuse to let you sell your product. The right to sell food isn't as strongly protected as the right to political expression.
> On Friday, the 9th U.S. Circuit Court of Appeals joined a slowly emerging consensus among the federal circuits, holding that governments have the right to mandate corporate speech “if the information in the disclosure is reasonably related to a substantial governmental interest and is purely factual.”
The latter requirement does not seem to be held in the case of compelling rsync to post an updated warrant canary claiming not to have received a warrant if they have.
Furthermore, in the case of cancer warnings, the actual law is phrased as:
> No person in the course of doing business shall knowingly and intentionally expose any individual to a chemical known to the state to cause cancer or reproductive toxicity without first giving clear and reasonable warning to such individual
so, it's not so much compelled speech "out of the blue", rather it's a requirement of doing business. There are other ways the business can comply with the law, such as not including the chemical in the product. In the case of warrant canaries, I'd be surprised if there's a similar law requiring them to be posted to do business.
I think the danger here is the interpretation of the prohibition on telling people you've been served with a secret warrant.
Whilst you seemingly can't force someone to do something the fact that not doing that thing is effectively telling people you've been served a warrant is grounds at least to take you to court.
I can only imagine this canary process being manual, if it were automated I'm unsure it could be considered speech (obvs: IANAL).
Until tested in court it's up in the area.
[0] - or at least I'm non-US