It originally was an insult used by communists against other communists to refer to people who supported the Soviet intervention into Hungary when the Hungarian government was collapsing. The Soviets intervened militarily to not only stabilize it but obviously make sure “their guy” would be in charge of the new government.

The communists who disagreed with this argued that Hungary should just be allowed to sort out their own government and the USSR shouldn’t be making those decisions for them, and they called people who disagreed “tankies” in reference to visible tanks in the streets when the Soviets showed up.

The word was then adopted by anarchists as an insult against Marxists, because Marxists believe in using state force to build socialism/communism while anarchists think the state is inherently a force for bad. This meant that “tankie” no longer referred to just the Soviet usage of tanks in Hungary specifically, but began to be used by anarchists to criticize every time a state ran by a Marxist party used state violence (“tanks”).

Liberals later discovered the word “tankie” and adopted it as just a synonym for “communist,” and the word has pretty much devolved in its usage in recent years to largely just be a stand-in for “communist” but more derogatory.