Whenever the majority of a society democratizes an issue, watch out. Those who advocated for the rule of the majority enforced by government better pray that they always remain in the majority. Once the center of opinion switches and the opposition ascends to power, the same process that worked wonders is now your worst nightmare.
A compulsory system of education controlled by the majority through government is a double-edged sword. It cuts in your favor when you are a member or fellow traveler of the ruling coalition, but it as easily dismembers your gains once power changes hands in a subsequent election.
If the fear is that the radical left will use public education to inculcate Mexican culture throughout the western states, the position should not be to strengthen public education while a more-moderate majority exists since all you will be doing is creating the beast that will ultimately destroy you -- Hegelian Dialectics.
And why shouldn't the radical left, or any group for that matter, work the system in order to use public schools for their purposes? We have been having a running debate as to how government can best indoctrinate for our purposes.
Many of our Founding Fathers came to the realization that decentralized control is the only way to guarantee Liberty. A market system of education would solve the indoctrination battles and allow us to live as free Americans. The founders of our great country were all educated privately, and their diverse opinions and heated debates guided the creation of our founding principles, which are forever documented in the Declaration and Constitution. We did not need a party-line to beat Liberty into the minds of the Patriots.
With greater effort, spread the ideas of Liberty. Otherwise you are educating the masses to accept centralized control. Once that has been accepted, if it already hasn't, it very easy to turn from one side of control to the other. Ludwig von Mises showed conclusively that Nazism and Marxism are not continuum opposites, they are simply collectivism and socialism in different packages. In fact Mises notes that Hitler favored ex-communists since their ideas of control were similar to his.
Liberty my friends, Liberty.