It does not matter that defense is a legitimate role of national government and that education is a questionable role of national government. (Since powers not specifically assigned to the fed are left to the state or to the people, that makes education an issue that locals can enact if they so desire.)
A person who works in either should not be assumed to be a sell-out just because they receive a government check.
Does that help you understand the difference between being a soldier and a government teacher in our nation's socialist schools?
By the way, I have never used the expression “sell out”. I merely state that working in a government owned and run socialist K-12 school is in complete conflict with conservative and Christian values and principles.
Do I need to restate the reasons again?