Hobby Lobby, the arts-and-crafts chain whose devout Christian owners won a landmark Supreme Court ruling on religious freedom, is caught up in an antiquities-smuggling scandal that has opened the company to accusations of hypocrisy.

The Oklahoma City-based business agreed to pay a $3 million fine Wednesday over its role in what federal prosecutors said was the smuggling into the U.S. of ancient clay tablets, seals and other Iraqi archaeological objects that might have been looted from the war-torn country.

Online, many people piled on, with more than one saying things like: "I know Hobby Lobby...