That's true, all ideologies are combination of right and left views. The history of where right and left came from is the french revolution. The monarchy is the right since they upheld traditional values. They called them the right because they sat on the right or some crap. The left were the revolutionist who overthrew the french goverment because they wanted equal rights for the people. Left simply means they want equal rights for all citizens nothing more. How you achieve each of these is then the ideology which generally tends to be considered a mix, however in the end they usually consider the ideology to be overall left or right. The Nazis were considered far right, "nationalism" is right and "socialism" is left ideology, but nazism together is more far right. I don't think Hitler believed in equal rights and he didn't like left ideology and wanted to uphold traditional aryan values.
Any type of change or anything that attempted to make ppl equal was a left movement. The american revolution for example, was a left movement. The civil rights act in the 1960s was also, they changed the traditional values and sought equal rights. Hitler didn't like left politics, he also didn't really believe in equal rights for everyone.
You are right though, you can be left and hate communism, nothing is black and white. You can be right and hate nazism. There is more than one way to accomplish a goal. If you watched the news though like you said they put both sides against each other, when in reality everyone has views on both sides and they likely may not even realize it.