Is it illegal to take a picture of a statue and list it online?

A statute in a public park is meant to be seen by the public and I doubt it can be copyrighted. A statute in a museum or private collection may have an expectation of privacy, but a photo of it may not necessarily mean it is a copyright violation. (In some situations, the museum may have copyrighted the material, but that is unusual). You can very easily check to see if these people do have the copyright; access the Library of Congress and see if the statute (by its name) is copyrighted and by whom (such as the original sculptor).
If it is not the people contacting you, then they are running a con and should be reported to the police.
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LEGAL DISCLAIMER
Mr. Sarno is licensed to practice law in NJ and NY. His response here is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. Mr. Sarno strongly advises the questioner to confer with an attorney in their own state to acquire more information.