By Mica Rosenberg

MEXICO CITY, May 17 (Reuters) - A couple who both changed their sex married on Saturday in Mexico's first transgender wedding, as the traditionally conservative country loses some of its inhibitions.

Mario del Socorro, formerly Maria, and Diana Guerrero, who used to be Jose, held an austere ceremony for friends and relatives in a community center.

The couple said they hoped media coverage would pressure Mexico's Congress to pass a proposed law that would let people get sex change operations in public hospitals and then be able to change their names and genders in public records.

"When you are applying for a job and your documents don't coincide with what you look like, you just don't get hired. It's that simple," said del Socorro, 55, who is balding with a wispy goatee and stands several inches shorter than his new bride.

Lawmakers behind the transgender proposal are challenging a swath of conservative customs in largely Catholic Mexico, and in recent years they have been gaining momentum.

In 2006, gay civil unions were legalized in Mexico City and the northern state of Coahuila.

Lawmakers in the capital last year legalized early-term abortions and approved a law allowing terminally ill people to refuse treatment.

The Catholic Church has strongly criticized all of these measures.

Del Socorro and Guerrero got married under their pre-sex change names because the law allowing gay civil unions does not give partners the same benefits as a traditional marriage.

At the ceremony, guests cheered the teary-eyed groom and beaming bride as they cut two tall wedding cakes before a crowd of journalists.

Members of the bride's Catholic family said the couple tried for months to find a priest that would marry them in a church.

"At the end of the day, it's a marriage between a woman and a man, so what's the problem with blessing this union in the eyes of God?" said the bride's sister, Flor Guerrero. (Additional reporting by Michael O'Boyle; editing by Jason Lange and Mohammad Zargham)

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