Neither humanity nor the Federation are run by a military government. I’m not even sure what gave you that impression. The federation, as its name suggests, is a federal system like the US, or the EU. Each planet retains its political structure while participating in the federation. Earth is the exception where it’s essentially the DC of the federation and is run directly by the federation council. Earth is also unique in being communistic rather than having a currency based economy like most other planets and the federation itself. Starfleet is a human organization that predates the creation of the federation and at that time was absorbed as its military arm. The president of the federation is the commander in chief of Starfleet. There is even a two parter in DS9 where an admiral tries to overthrow the president and fails and it is referred to as a “military coup”.