What minimal means is subjective.
I'm not opposed to a government role in education, nor do I think not being opposed is incompatible with libertarianism. I've got plenty of problems with the government school system, but we live in the world as it exists and for some people the best option available is the one attached to government, regardless of what got us here.
Minarchists will always draw the lines differently, even among one another, because value is subjective. Taxation is theft, but there are also things worse than theft. When I say taxation is theft it's meant as a call to minimize it and what government uses it for, because there's a moral component to government revenue based on a lack of universal consent. I don't mean that we should have zero taxation or zero government services. Utilizing a school system isn't really functionally different than using government roads.
I also plan to take social security, like Ayn Rand.
What is true is that a libertarian is defined by one who advocates merely a minimal state intervention in people's personal and economic lives. What is true is that one can support a state role in education while still being for a drastically minimized state, especially compared to what we have now.
If I could press a button and, say, end the department of education, I'd tap that. If I could press a button and end all government involvement in education without anything positive to immediately replace it, I wouldn't.