I didn't mention anything about the size of the demography. I just mentioned what the demography was.You are overestimating the demographic size and influence of the US far right. The US military is also definitely not that dominated by the far right otherwise both the US and the world would be in much worse shape.
US military servicemen of certain demographic are in fact dominated by Far Right ideologies. The difference is that the partisan thought may not extend all the way upto the top of the hierarchy OR IS subdued and neutered as the final decisions are taken by the Congress.
I reiterate as well list some other things I think -
1. A huge portion of Military servicemen are from well to-do middle class and even upper middle class families. They are led by Alpha-male-culture who sees the military service as a rite of passage and a badge of honor. They are also guided by patriotism.
2.The least partisan ones fights for the "Constitution".
3. Hispanic people are increasingly filling up numbers in the military.
4. Most of the military servicemen are Pro-Reagan (lately Pro-Trump), Pro-NRA, Non Hispanic while males.
5. Do read up how the name " Eddie Gallagher" is perceived within the US military ranks and how this name can incite discussions within the community.
6. Military Culture is different but related to US culture(s).
7. Race relations are improving day by day in the military. Problems were severe half a century ago and there was heavy segregation (like in civilian life)BUT now it is isn't. Of course, African origin military men have developed their own sub-culture that has tales of Tuskegee Airmen, Unionists vs Confederates fights etc to offer buoyancy and support. (They cheered for Obama)
To sum up - US military is dominated by Right wing. Whether it is far-right or not needs survey.