There is no law that prevents them from posting a sign saying you are not allowed. Is it childish, stupid, and poor business? Yes. Is it illegal? Nope.
I would just go in sometime when they are not busy and apologize and ask that they remove the sign. Good luck.
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.
Put this in a letter to the editor of the local newspaper and you can be pretty sure the sign will come down. Of course, that depends on how you word the letter.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
Nothing stops a business from excluding a named person from their premises, and nothing stops the business from posting notice of that. If the notice contains provably false damaging information about you, posted with knowledge of the falsity or in reckless disregard of the truth, then you might be able to sue for money damages or for the sign to come down. But, if the sign contains no provably false damaging information, then you have no lawsuit. In that case, I would follow the advice of the other attorney and try to use persuasion to get the store to reconsider the posting of the sign. If the store continues to refuse, remember that you also are allowed to post signs about them, on your own property, and you can write newspapers, etc. with criticisms of the business, under the same terms: nothing you know to be false or made in reckless disregard of the truth.
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If the contents of the sign do not state false facts then no law prevents them from posting it. If it states false facts then it might be defamatory. But if all it says is you are not welcome, then that is not a statement of fact upon which you could sue. Why not organize some friends to boycott the store for their business practices and see if you can get them to bring the sign down.