For the common civilian it probably would have to do with the fact of fear mongering during the Cold War. Our military was trained that communist regimes were our enemy. For decades our Gov't blasted the USSR and communism and everything associated with as evil.
So when a person hears something over and over and over all the time, they tend to believe it. Though I would think that our Special Forces and more highly trained military personnel would have more of a grudging respect due to the similarity of service?
But way back in my early 20's when i got my head out of my azz I took a better look at the world around me and realized that our Gov't isn't necessarily giving us accurate information.
So I don't really relate to hatred of others just for the sake of it. I would say just as I am impressed and proud of our Special Forces and the same could be said of the Spetnaz - they are all some truly dedicated and talented folks that do what very few can.