IANAL, but I couldn’t find any legal precedent, let alone a SCOTUS ruling, on whether the First Amendment covers ignoring a sign on private property to not knock (or ring) as protected speech. The relevant case law all seems to address municipal ordinances, not private property rights. Which makes sense, as who in their right mind would sue a private citizen over their right to futilely bother them, let alone pursue it all the way to the Supreme Court?
Unfortunately The Free Speech Project article @Skeptic linked to seems to make the leap from said case law to the conclusion that the First Amendment covers ignoring a sign posted by a private citizen on private property, when in fact the case law would not seem to support a conclusion either way.
So what does that mean for John’s “No Soliciting” sign in the Seattle suburbs? In short, it is irrelevant to noncommercial home visits, be they for the purpose of religion, government, or politics.
What the anecdote does show, however, is that John’s harassment of the article’s author Honl-Stuenkel exceeded merely demanding the author leave his property to a blatantly unjustified assumption of authority over his neighbors’ private property, making John the kind of Darren that makes a neighborhood a worse place to live.
While The Free Speech Project seems to have a mission I support, I’d be more inclined to deffer to their legal interpretation if they listed any law degrees on their seemingly exhaustive list of contributors, but the only law school experience they list is two past contributors currently pursuing law degrees. It seems like a project such as this would benefit enormously by having a J.D. (preferably specializing in First Amendment law). Not least of all because I would be fascinated to read a professional opinion on whether or not the case law actually does support ignoring private property signage against knocking (or ringing) as protected speech. My instincts suggest it’s not but, again, IANAL.
The Free Speech Project

Contributor Bios - The Free Speech Project
This webpage seems to have a more thorough list of case law and clearer analysis, and even there I couldn’t find any cases that weren’t about municipal ordinances:
The Free Speech Center

Door-to-Door Solicitation
Door-to-door solicitation by political parties, religious groups, and businesses can lead to clashes between First Amendment freedoms and homeowners’ privacy rights.