What is the significance that the cattle is of mixed breed?

Josiah's mixed-breed cattle are white with brown speckles. They form an obvious symbol of racial mixture and change. Tayo himself is the product of just such a mixture, being born to a white man and a Laguna woman. For this, he earns the undying enmity of Emo. Josiah himself wants to create a new breed of cattle, one that will survive the harsh droughts of New Mexico. So he gets the idea of breeding a meaty Hereford bull with the hardy but much thinner desert cattle of Mexico. It is hoped that the end product will be a stronger, meatier cow able to withstand adverse weather conditions.
The new breed of cattle planned by Josiah symbolizes how life is changing in the Laguna Pueblo community. The racial makeup is changing, and Tayo is a living example of this. Josiah's bold experiment in animal husbandry starts to pay off, confirming Tayo in his conviction that change is not just inevitable but a good thing and will help to ensure the survival of the community.