Milenio today reports that deputies from the PRD have asked the Secretary of Gobernacion to go after the Catholic Church for expressing its views on gay marriage in D.F. According to the PRD, the Catholic Church has violated the Ley de Asociaciones Religiosas y Culto Público (LARCP) which carves out a legal space for religious organizations in Mexican civil society.
The original reforms took place under the Salinas administration's very classical liberal drive to codify all segments of society, as well as their efforts to show the U.S. before and during NAFTA talks that Mexico could extend the rule of law to all areas of society. In short, it was Salinas de Gortari's way of signaling to the world (remember, he was gunning for UN or IMF positions at that point in time) that Mexico was "civilized" and that El Presidente was the grand reformer and modernizer of Mexico. Religious rights were human rights, as was argued at the time, and Mexico had a duty to protect those rights.
Move forward almost two decades, and we find ourselves in a conundrum. D.F. seeks to protect the civil rights of homosexuals to enter into the marriage contract (above all a civil act in Mexico - as thousands of dead liberals and conservatives can attest). The Catholic church seeks to excercise its rights to object without legal retribution - as laid out in the 2006 version of LARCP (Article 2, subparagraph e).
The PRD position is weak, but reforms in 2006 to the law could help their cause. Article 8 requires that churches "fomentar el diálogo, la tolerancia y la convivencia entre las distintas religiones y credos con presencia en el país." While you might argue that isn't the same as tolerance in general society, in combination with Article 14, it might have some punch. Article 14 states that "Tampoco podrán los ministros de culto asociarse con fines políticos ni realizar proselitismo a favor o en contra de candidato, partido o asociación política alguna." Taking a public stand against gay marriage might be seen as a violation of this portion of the law.
Finally, throughout the document the state reserves the right to protect the rights of third parties. Is it then the state's duty to mute the Catholic Church if the speech of the church could result in legislation that restricts the rights of a third party? My own U.S. history demonstrates that only the right of the central state is powerful enough to protect the rights of minorities - but the central state has also acted to protect the hateful language of those who would seek to terminate the rights of minorities. And the big gun, Article 29: "Convertir un acto religioso en reunión de carácter político." That statement is as loaded as Amy Winhouse.
I would tend to see the PRD as hunting flies with vinegar by taking this approach, and restricting speech to protect other rights seems counterproductive to civic society. I'd also point out that Mexico has "tolerated" plural marriage for the indigenous and quirky religious groups, as well as a mind-blowing amount of cohabitation for decades (well...centuries). The Catholic Church has complained the whole time, and those outside the reach of the Madre Iglesia continue on their way.