When I discuss this poem with my students we do wind up having strong conversations over these notions of Indigenismo and Meztizaje and in these conversations I'm always reminded how complex identity is.
Despite that, I still think it's important to explore the very questions you raise here, and I'm going to try to incorporate that in my future lectures.
The emphasis on mestizaje has led to the belief that Mexicans and Chicanos possessing tanned skin must be mestizo.
The implication that tanned Mexicans and Chicanos are partly descendants of Indian blood is implied in when Gonzales writes that the “chattering of machine guns are death to all of me: Yaque, Tarahumara, Chamula, Zapotec, Mestizo, Espanol”.
The implication is that such indigenous people make up all of “Corky” Gonzales, who is Joaquin, who embodies all Chicanos.
Indigenous blood as a requirement to identify as Chicano is limiting to those without it and leads to inaccuracies when self-identifying.
Also, your claim that the poem implies that "one must be a hybrid to qualify as Chicano" also seems based on a either/or perspective which I don't believe is effective. I understand why the Chicano movement wanted to distance itself from European influence.
The poem never states that the reader "must" do anything and should be read more as a metaphorical/philosophical exercise and I don't think your critique needs that statement to be true in order for it to be valid. Again, I was impressed with your critique; you can tell by the length of my response. You definitely gave me some new perspectives to consider! For personal reasons, I only wish Corky wouldn't have strongly implied mestizaje is the basis of Chicano identity.
For Paz, the “Mexican does not want to be either an Indian or Spaniard. By pegging Chicano identity to mestizaje, Gonzales has tied Chicanos to an identity rejected by many Mexicans, and which is a source of conflict to the mothers and fathers of Chicanos: Mexicans.
In his book , Luis Valdez describes mestizos as a “powerful blend of Indigenous America with European-Arabian Spain, usually recognizable for the natural bronze tone it lends to human skin” (xiv).