When I'm asked where libertarians fit on the left-right spectrum, I say we don't. We're above the line.
For more than 220 years - from the 1620s to the 1840s - most American schooling was independent of government control, subsidy, and influence. From this educational freedom the American Republic was born.
When power replaces truth as the goal, assertion replaces reason as the path
Some want prayer in school, some want condoms. Printing prayers on condoms satisfies nobody.
Charter schools are just public schools on a slightly longer leash. A dog on a long leash is still a dog on a leash.
In all countries, in all centuries, the primary reason for government to set up schools is to undermine the politically weak by convincing their children that the leaders are good and their policies are wise. The core is religious intolerance. The sides simply change between the Atheists, Catholics, Protestants, Unitarians, etc., depending whether you are talking about the Soviet Union, the Austro-Hungarian Empire, America, etc. A common second reason is to prepare the boys to go to war and the girls to cheer them on.
The combination of both legs leads to social harmony and material abundance.
I proclaim publicly that I favor ending government involvement in education.
The Left/Right scale is a misleading way of comparing political systems. It doesn't measure anything.