The law has changed several times since the mid-1950s. Most recently, in 1998, Mexico permits Mexican citizens to have more than one (Mexican nationality). As for renouncing other citizenships, I asked and was told that the distinction applies to being on Mexican soil. As a Mexican within Mexico, you abide by the laws and benefits, and cannot claim another. So, break a Mexican law as a dual citizen, means you are treated as a Mexican citizen.
Here's the text: Desde 1998 la Ley de Nacionalidad de México permite que las personas mexicanas cuenten con otra nacionalidad además de la mexicana. Este hecho reviste gran relevancia porque, en efecto, la doble (o múltiple) nacionalidad implica una ampliación de derechos para la persona que cuenta con ella.