The words Mexican and American and 175 like adjectives (based on U.N. membership) refer, in general, to nations and their culture and, when applied specifically to people, denote citizenship and associated ethnicity.
The story of America is not about immigrants importing their culture. America is about individuals purposely choosing to leave behind 176 other nations with inferior cultural values and attitudes toward personal liberty and individual rights in order to adopt America's.
It used to be that legal immigrants wanted their children, as quickly as possible, to be ethnic Americans, indistinguishable, in language, cultural habits and philosophical beliefs, from those Americans already here, so they could share fully in the bounty America offers its citizens.
In the 1960s the intellectual left began altering the traditional process of assimilation by promoting the concept of multiculturalism. The justification offered for change was it would enhance certain individuals' self-esteem.