What is the name of the primary symbol, which is now outlawed outside of the context of art or science, and was widely used even on the state flag?
Strafgesetzbuch section 86a The German "Strafgesetzbuch" (Criminal Code) in § 86a outlaws "use of symbols of unconstitutional organizations" outside of the contexts of "art or science, research or teaching". This concerns Nazi symbolism in particular and is part of the denazification efforts following the fall of the Third Reich.
Ceremonial deism Ceremonial deism is a legal term used in the United States for nominally religious statements and practices deemed to be merely ritual and non-religious through long customary usage. Proposed examples of ceremonial deism include the reference to God introduced into the Pledge of Allegiance in 1954, the phrase "In God We Trust" on U.S. currency, and the Ohio state motto, "With God, all things are possible".