An idea that may have merits so long as a feasible alternative can be proposed but surely not the best place to start when trying to increase the liberty of the country or convince others of the merits of free market and a limited republic. There are so many other egregious violations or liberty (e.g. banking, government spying, corporate lobbying, bailouts, military industrial complex, gerrymandering, gun bans, TSA, free speech zones, militarized police, ...). And talking about abolishing public schools is a quick way to get marginalized and written off as a quack by 90% of citizens. Probably better strategically to focus on areas where there are at least allies and the battle is winnable.
You'd have to ease people into it for sure.
Start by abolishing the Department of Education. That's something Republicans have talked about many times (But do they, when they have the ability). Return all education choices to the states.
The states could then kill their Department of Education, giving power to the county level. Now citizens could be given a huge portion of their money back if a city decides to remove education from their property taxes. This would appeal to many.
other egregious violations or liberty
Those are good goals too!
Maybe neither side cares about whether their preferred characters deserve to be there but instead just want the schools to be propaganda--so long as it supports their side.