The right wing of the CPGB that supported the counterrevolution in Hungary were not "Orthodox communists." You seem to think Marxism is a purity-based moralist doctrine, but in fact the right-wing supported a fascist movement and a destruction of worker power. The Hungarian revolt in 1956 was infested with anti-semitic pograms. MI6 funded, supplied, and trained the Hungarian counter-revolutionaries. These counter-revolutionaries were allied with fascists who were lynching Jewish people and Communists. The Truth About Hungary by Herbert Aptheker heavily relies on citing western sources like the New York Times. Aptheker backs up his claims heavily.

"The special correspondent of the Yugoslav paper, Politika, (Nov. 13, 1956) describing the events of those days, said that the homes of Communists were marked with a white cross and those of Jews with a black cross, to serve as signs for the extermination squads. “There is no longer any room for doubt,” said the Yugoslav reporter, “it is an example of classic Hungarian fascism and of White Terror. The information,” continued this writer, "coming from the provinces tells how in certain places Communists were having their eyes put out, their ears cut off, and that they were being killed in the most terrible ways."

"But the forces of reaction were rapidly consolidating their power and pushing forward on the top levels, while in the streets the blood of scores of massacred Communists, Jews, and progressives was flowing."

"Some of the reports reaching Warsaw from Budapest today caused considerable concern. These reports told of massacres of Communists and Jews by what were described as 'Fascist elements' ...." (N.Y. Times, Nov. 1. 1956)

"The evidence is conclusive that the entry of Soviet troops into Budapest stopped the execution of scores, perhaps thousands of Jews, for by the end of October and early November, anti-Semtic pogroms - hallmark of unbridled fascistic terror - were making their appearance, after an absence of some ten years, within Hungary."

"A correspondent of the Israeli newspaper Maariv (Tel Aviv) reported:

During the uprising a number of former Nazis were released from prison and other former Nazis came to Hungary from Salzburg . . . I met them at the border . . . I saw anti-Semitic posters in Budapest . . . On the walls, street lights, streetcars, you saw inscriptions reading: “Down with Jew Gero!” “Down with Jew Rakosi!” or just simply “down with the Jews!”

Leading rabbinical circles in New York received a cable early in November from corresponding circles in Vienna that “Jewish blood is being shed by the rebels in Hungary.” Very much later-in February, 1957-the World Jewish Congress reported that “anti-Semitic excesses occurred in more than twenty villages and smaller provincial towns during the October-November revolt.” This occurred, according to this very conservative body, because “fascist and anti-Semitic groups had apparently seized the opportunity, presented by the absence of a central authority, to come to the surface.” Many among the Jewish refugees from Hungary, the report continued, had fled from this anti-Semitic pogrom-like atmosphere (N.Y. Times, Feb. 15, 1957). This confirmed the earlier report made by the British Rabbi, R. Pozner, who, after touring refugee camps, declared that “the majority of Jews who left Hungary did so for fear of the Hungarians and not the Russians.” The Paris Jewish newspaper, Naye Presse, asserted that Jewish refugees in France claimed quite generally that Soviet soldiers had saved their lives."

Further, the CIA also backed Hungarian resistance forces:

Prague in 1968 was a similar fascist uprising in both cases there were some elements of progressive protest, but these were greatly overshadowed by the fascist movements. Dubcek wanted to sell out to the IMF, and restore capitalism. The idea that any of this was about "democracy" or "freedom" is silly, it was always about Cold War tactics to destabilize socialism.

TL;DR imagine if the January 6th rioters were armed and trained by foreign governments, started lynching officials and Jewish people, and the US sent in the army to put down the insurrection. The MAGA chuds would claim that it was about "freedom" and "democracy," but we all know that they just wanted Trump in office.

Regarding the Tian'anmen protests, a color revolution grew from what originated as protests against the marketization shifts under Deng Xiaoping that had turned into western-backed protests against CPC control, resulting in a few hundred deaths from clashes between rioters and the PLA around Beijing after the PLA had been sent in to disburse the protests. Once the PLA reached Tian'anmen Square, the center of the protests, the square was dispersed bloodlessly. The CIA-backed student leaders were evacuated in Operation Yellowbird. For more, I recommend this Tian'anmen Protests reading list.