The term originates from controversy among UK Communist labor-unionists over support of the Soviet Union, in its violent occupation of dissenting Communist countries Hungary and Czechoslovakia — when Khrushchev sent tanks to suppress popular revolutions against Soviet control of their countries.

Notably, this was Communist-on-Communist violence: the revolutionary Hungarian and Czechoslovak regimes were still run by their Communist Parties. Thus "tankies" were, originally, Communist labor-unionists who endorse or tolerate violent suppression of other Communists to secure the power of the Soviet Union.

https://en.wikipedia.org/wiki/Tankie

More recently it's been used to refer to supporters of authoritarianism in China, which is associated with tanks by way of the 1989 Tienanmen Square massacre.

https://en.wikipedia.org/wiki/Tank_Man