One could make an argument that The Boy Scouts of America and their ubiquitous summer camps are political. Although not overtly right or left, they do (again, arguably) espouse a quasi-military model, which tends to lean in the direction of the Right. (Did I include enough caveats to avoid a mini-debate? Eh, this being the SDMB, probably not!)
Military model Like the Red Guard and the Peoples Liberation Army? The Russian Young Pioneers was consciously modeled on the Scouts, but then, the Communist Party cell structure was consciously modeled on the Christian Church.
One can make an argument that the personal is political, but it would be hard to make an argument that the BSA makes you vote Republican.
Your confusion stems from the fact that the fascists were militaristic, and the fascists were opposed by the socialists, because the fascists were a branch of the socialists, competing on the same ground, so the hard left is opposed to the fascists, who support the scouts, so the scouts must be opposed to the socialists …
In the US we primarily rely on the liberal arts university system for such political indoctrination.