The term Mexican referred to anything originating from the Earth nation of Mexico.
An establishment offering Mexican food existed in Los Angeles during the late 20th century. (VOY: "Future's End")
In 2366, James T. Kirk personally handpicked some prime Mexican red chili peppers for Space Commander José Dominguez. (TOS: "The Man Trap")
In 2375, Miles O'Brien and Julian Bashir contested whether or not the aged Davy Crockett should have surrendered at the Battle of the Alamo in 1836, Bashir citing that "Crockett was 49, quite old for the standards of the time. His days as an Indian fighter were well behind him. This is not a man about to fight to his last breath. He was out of ammunition, the Mexican Army was storming the battlements. He would have surrendered. It's as logical as that. Simple." (DS9: "Once More Unto the Breach")