One needs to look no further for validation of this than to look at a man who spent his entire life fighting Communism - Adolf Hitler. Hitler, a far right Fascist leader gave his life uniting Europe against the Soviets. In his book, Mein Kampf, he explains why he hated Communism in chapter 2 :
"The Jewish doctrine of Marxism repudiates the aristocratic principle of Nature and substitutes for it the eternal privilege of force and energy, numerical mass and its dead weight. Thus it denies the individual worth of the human personality, impugns the teaching that nationhood and race have a primary significance, and by doing this it takes away the very foundations of human existence and human civilization. If the Marxist teaching were to be accepted as the foundation of the life of the universe, it would lead to the disappearance of all order that is conceivable to the human mind. And thus the adoption of such a law would provoke chaos in the structure of the greatest organism that we know, with the result that the inhabitants of this earthly planet would finally disappear.
Should the Jew, with the aid of his Marxist creed, triumph over the people of this world, his Crown will be the funeral wreath of mankind, and this planet will once again follow its orbit through ether, without any human life on its surface, as it did millions of years ago.
And so I believe to-day that my conduct is in accordance with the will of the Almighty Creator. In standing guard against the Jew I am defending the handiwork of the Lord.
"
"numerical mass and its dead weight" is a clear reference to Communism principles of democracy, where one person one vote, no matter your race.
See...the USA being part of the protagonist of the cold war would of course structure its history classes to hide certain facts so that you do not see the world the way it was seen prior to the cold war.
You can get Hitler's book online but please, do not turn into a right wing after reading. Use it to understand why the right hates the left.