Church, Politics and State Education Systems

[DuncanONeil]

The US military punnishes its members if they do anything that can be construed as being politically orrientated as support for one party over another. Why not hold teachers to the same standard?

The above statement is not quite accurate. There is no article in the UCMJ that addresses this issue, at least directly.
But members are bound to avoid partisan political activity, largely because of the color of authority. Same reason the fraternization rules exist, although that is spelled out in the UCMJ, and gambling with subordinates.