I find that highly unlikely. I believe you have been misinformed. A state would not bother to make laws regarding membership in a private organization. Please list those states which you claim have such laws and post just one of those supposed laws.
He is not misinformed. Many states have similar laws.
Michigan Law states:
Unlawful Use of Name and Insignia:
Whenever there shall be an actual or threatened violation of the above act, an application may be made to the court or judge having jurisdiction to issue an injunction upon notice to the defendant or defendants of not less than 5 days, for an injunction so restraining such actual or threatened violation, or if it shall appear to such court or justice that the defendant or defendants is or are in fact using the name of a military, ex-military, patriotic, benevolent, humane, fraternal or charitable corporation or organization, or a name so nearly resembling it as to be calculated to deceive the public, or is wearing or exhibiting the recognized or established badge, insignia or
emblem of such corporation or organization without authority thereof and in violation of the above act, an injunction may be issued by said court or justice enjoining or restraining such actual or threatened violation, without requiring proof that any person has in fact been misled or deceived thereby.
There are a few other laws in Michigan with similar wordings, and a few laws pertaining specifically to Freemasonry.