You can use the word ideological to describe shared ideas or beliefs, and the word breaks down to ideo- (not "idea," but close) and -logical. An ideological stand for equal rights made Rosa Parks stay in her seat at the front of the bus.
Ideological is an adjective that describes political, cultural, or religious beliefs. An ideology is a body of ideas, and those who agree with the main idea of something take an ideological stand to support it. Unlimited freedom is a strong ideological belief in countries like the United States, and communism was once the ideological foundation in parts of Europe. Some follow ideological ideals that are logical, while others take stands that seem, well, idiotic or illogical, like racism.