During the course of the cold war, there were many countries that chose not to side with either the USA-led western bloc or the Soviet-led eastern bloc, instead joining with what is known as the Non Aligned Movement(NAM), an organization for countries that did not formally sided with either blocs. Usually, both sides ignored these countries.
But what if the US and the USSR declared that there will be no neutral countries allowed, stating that "you're either with us, or against us". Any countries that tried to remain neutral would find their leaders secretly overthrown, or outright invaded.
How would this affect the cold war?