Re your request for input: I can't tell you how Hungary '56 influenced British politics, for example (though I think you know it played a part in Eisenhower's decision to rein back Britain and France in the Suez invasion).
But, for me personally, Budapest '56 was the first international event that penetrated my consciousness. I'd heard plenty of talk about The War, of course, but I knew that was in the past. I can't say I learned a lot about Hungarian events, just about the Soviet tanks crushing the revolt and killing people. (My sources were the radio, the local newspaper, and above all my parents' conversation). I later learned to situate it better in the course of history. But even in outline, Budapest '56 remained with me as a kind of base on which I built an intuitive opposition to Soviet Communism (Prague '68 was therefore "only" a repeat performance, a reminder).
Baby boomers in general did not support Stalinism. It was impossible, even for those who thought of themselves as revolutionaries, to develop a romantic attachment to the Sovs (as the nineteen-thirties generation had). You might be Trot, or Maoist, or anarchist, autonomous, instant-karma people's-justice barrel-of-a-gunner, whatever -- but no one thought the Russian revolution was a positive model. The sufferings of the Hungarian people were (though not the only influence) probably the turning-point in left-wing attitudes to the Soviets.
Your comment about left-wing attitudes toward the Soviets reminded me of it.
The latter make me post something that is not debating what you wrote, but something I left off this diary because it was long enough already.
Sometimes 1956 is lauded as such, I don't think one could say in general that 1956 was 'the end of communism', or 'the end of belief in communism', or 'the end of Western symphaty for the Bolshevik experiment', or some other variant.
