Unfortunately, many of their cultural practices have been lost over the past few hundred years. Native cultural traditions in the Americas were adapted to account for the huge influx of Spanish colonists that brought their own cultural traditions from Europe. However, it was by no means a smooth transition. The Spanish were very brutal, and even went as far as to build Catholic churches on top of native temples. Many times, they attempted to eliminate native cultural traditions and religions all together. They forced natives to build churches, gave them Spanish names, and attempted to covert them to Christianity. Spanish monks saw native traditional dances as satanic worship, and then condemned them. There are also a few accounts of benevolent monks who worked alongside natives to help promote their communities and teach them the Spanish language, but as a whole, the Spanish were set out for conquest.
However, the common people prevailed, and Spanish colonists and native people in almost every region in Mexico and Central America married and integrated with one another over the course of several generations. They melded their cultural traditions from both European and native cultures to create new traditions, new dances, new songs, new foods, and new styles of dress. What evolved was a mosaic of traditional foods, dances, and dress that are still being kept alive today.
In 1950's Mexico, the mestizo (or mixed) traditional cultural practices were incorporated into formalized institutions of folkloric ballet dance, such as the Ballet Folklorico de Mexcio de Amalia Hernandez. This dance institute perfected regional dances from cultures throughout Mexico, and the institute performs regularly at El Instituto Nacional de Bellas Artes (The National Institute of Fine Arts) in Mexico City. They also travel the world sharing these unique mosaic dances from Houston, to London, to Shanghai. Although these dances may seem to be original cultural dances on the surface, in actuality they represent a hybrid of older traditional native cultural practices and older European practices.
In many ways you could argue that the cultural practices of both cultures are being preserved by Mexican ballet institutes, but on the other hand, both cultures have lost their separate and unique traditions. It is fascinating that true culture and art in this sense is never lost, and if you look closely, you can still see remnants of the old cultural traditions today.
In contrast to Mexican culture, many of the cultural traditions of natives in the United States have been completely lost due to genocide, relocation, and assimilation. When half of a population is murdered, the other half relocated, and when children are punished for speaking their native language instead of English, swift elimination of cultural traditions soon follows. The cultural traditions of many of these people may eventually be lost, if not already lost all together.
As the world continues down a path of globalization, even in the most remote corners of the globe, people are more concerned with how they are going to feed their families, where they will find work, and how to adapt to new economies more so than continuing the cultural traditions of their ancestors.