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LGBT rights in Mexico and also tolerance and acceptance of gay, lesbian and transgender people varies quite a bit by the region or state. As a federal system, the important rights such as marriage and adoption are decided on a state by state basis and similarly to the United States, battles in court and state legislatures are taking place in different places of the country.
As well the indigenous cultures that are dominant in various areas of Mexico tend to have different attitudes to LGBT people and so that has influenced regional differences. As such outside the capital, the most progressive regions tend to be Oaxaca and the Yucatan
LGBT travelers will appreciate Mexico City's notably progressive attitude when it comes to sexual diversity. Informally, few cities worldwide could better represent the "live-and-let-live" attitude that is a (rarely remarked upon) feature of Mexican culture in general, further enhanced by the open-mindedness that city life supports. The generally warm, chatty and convivial nature of the Mexicans practically compels them to enjoy people as people, nothing more or less. There's a feeling that we're all in this together and a surprising lack of recourse to labels. As you make your way through the city you'll see open expressions of sexual diversity, gestures of affection and hand-holding that attract virtually no attention from passers-by, even outside the Zona Rosa.
In recent years this street-level attitude has played out in a series of city-wide legal reforms that are a source of pride to many citizens, gay, straight or otherwise. Most notably, in 2010 the DF (which acts like a state in Mexican politics) became the first jurisdiction in Latin America to legalize same-sex marriage. Other progressive reforms have included allowing transgender people to legally change their sex on birth certificates and other legal records. Discrimination based on sexual identity is illegal in any guise, and as of 2010, same-sex couples can legally adopt children.
The government also maintains support centers for the LGBT community such as its Centro Comunitario de Atención a la Diversidad Sexual, which focuses on guaranteeing community access to healthcare, HIV testing, human rights, safety and justice, serves as a referral to other public services and support, and even helps process same-sex marriage licenses.
Naturally there is more work to do and activists push for even greater advances; but in the meantime Mexico City's example might well serve other cities worldwide that seek to enhance equality for their lgbt citizens
Same sex sexual activity is legal in all of Mexico and has been since 1872. There is also a nationwide law banning discrimination in employment and housing which has been in effect since 2003.
Same sex marriage was been ruled a right for Mexicans by the Mexican supreme court in 2015 but due to the Mexican legal system this right has not yet been implemented in all parts of Mexico and couples may have to apply to the courts to override local rules. Wikipedia has a article listing the current state of same-sex unions in Mexico. The number of states which have implemented fully legalized same-sex marriage on demand (without a court petition) continues to grow (see map). Battles in other states are ongoing and in many cases several couples have been married due to court decisions but the precedent has not yet been fully established so that it would be freely available to all. And the Mexican Supreme Court has ruled that all 31 states must recognize same sex marriages performed in the states where they are legal.
Nationally, the president Enrique Peña Nieto stated in 2016 that he supports full national legalization and would introduce legislation. However, there is no specific timeline for this and since this announcement there has been significant pushback primarily from the Catholic church.
Other rights, such as adoption rights and the rights of transgender people vary by state.
The Mexico City section above was taken from Mexico City excellent LGBT Tourism Guide which is available for download here.