[Politicidal organizations]?, such as the Soviet communist government or the Chinese communist government, kill people who hold political views that conflict with the government's view.
Other organizations (shall we call them religiocidal organizations?) kill people who adhere to a particular religion, or to religions other than their own. Nazis constitute a good example of such an organization, having killed approximately 6 million Jews between 1939 and 1945.
Ideocidal organizations are a kind of homicidal organization.