How did the ideological differences between the former Soviet Union's communisim and American democratic capitalism increase Cold War tensions?
When Sting says, "We share the same biology regardless of ideology," he isn't kidding in articulating the vast level of difference between both sides in the Cold War. The previous thoughts were accurate. The difference in philosophies helped to both cause and exacerbate the antagonisms between both sides. The disparity in both thought sets struck at the very core of how individuals view their places in the world, the role of government, and the protection of individual wealth as opposed to the distribution of said wealth by a public element. These differences were challenging to overcome because of their profound nature, helping to define reality in a manner that caused both sides to not only protect and vault their own beliefs, but do so at the cost of "the other." These differences were ideological and really went far to prevent the other side from empathy and respect of "the other." In the end, this would be why the world has not seen the likes of such an antagonism where the world is divided into two camps with an intense dislike of the other.
You can argue that the ideological differences between the two sides was the whole cause of the Cold War. In this sense, it increased Cold War tensions because it helped to cause the two sides to distrust one another. This is especially true because the Marxist ideology held that capitalism must be overthrown in order to bring about a socialist society.
In general, then, the ideological differences made the two sides distrust one another intensely. This ensured that tensions would increase over time because each side would view all of the other's actions with distrust -- they would think that all actions were aimed at overthrowing them.