iAmerica's backyard is a concept often used in political science and international relations contexts to refer to the sphere of influence of the United States.
Not in my backyard or NIMBY is used pejoratively to describe opposition by residents to a proposal for a new development close to them. It is also used more generally to describe people who advocate some proposal but oppose implementing it in a way that would require sacrifice on their part.
The red flag is a symbol of left-wing politics, in particular, of Communism and Socialism.