Are you sure the movie isn't saying that all Natives of Central and South America are like Chihuahuas? Does it show any other animals representing Latinos or Natives? Does it show any Chihuahuas that don't have Latino or Native roots? Even Chloe the Beverly Hills Chihuahua gets in touch with her inner Latina, I believe.
Some history of Chihuahuas:
Historical records of the Techichi, which were thought to hunt in packs, can only be traced as far back as the ninth century but it is highly likely that this is the Chihuahua's native Mexican ancestor. Evidence of this is that the remains of dogs closely resembling, but slightly larger than the average Chihuahua have been found in such places as the Great Pyramid of Cholula, which dates back to the 2nd century BC and predates the 16th century. There is also evidence to suggest that the Techichi may also predate the Mayans. After the Toltecs were conquered by the Aztecs, it is believed that this early ancestor of the Chihuahua was adopted as a symbol of the upper classes and it has been suggested that they were used in religious ceremonies for the absolution of sins and to guide the spirits of the dead. In terms of size, the present day Chihuahua is much smaller than its ancestors, a change thought to be due to the introduction of miniaturized Chinese dogs, such as the Chinese Crested Dog, into South America by the Spanish.
Anthropomorphic movie animals
Let's see how other movies handle the issue of representing racial or ethnic groups with animals.
Compare Beverly Hills Chihuahua with The Lion King or Madagascar movies. The latter movies show a range of animals in Africa. They don't associate a single species--e.g., apes--with Africa's people. And they don't show the lone species dancing in grass skirts or waving spears like stereotypical Africans.
Or compare Beverly Hills Chihuahua with Kung Fu Panda. The latter represents Asians with a giant panda, a red panda, a snow leopard, a tigress, a monkey, a mantis, a viper, and a crane. Again, there's no relation between Asians and any one species. Because of the variety of animals, you can't infer that Asians are panda-like or tiger-like or monkey-like.
In contrast, Beverly Hills Chihuahua does equate Chihuahuas with Latinos and Latin American Natives. It does show them engaged in the stereotypical behavior of these people. I don't know how close the correspondence is between Chihuahuas and Latinos, but my impression is it's pretty close.
For more on the subject, see Aztec Animals in Chihuahua and Chihuahua Movie Is Stereotypical.
Below: "Yo quiero tacos, sombreros, y siestas aunque yo soy Indio y Chino y no Mexicano."