By definitions of words capitalism and communism are not conflicting ideologies unless applied to the extreme.

The dictionaries tell us this:

Capitalism means private ownership of production of goods and services.

Communism means worker owned production of goods and services.

Obviously you could argue that all Capitalism is Laissez Faire and that all communism is some abominable mix of Marxism and somehow dictatorship, but then we have no terms to describe the 99% of industries that fall anywhere in the middle as anything except "market system."