Look at Joseph McCarthy and see a counter-example. He used the exact same logic: to prevent a Soviet-style totalitarian government in the US, we had to be intolerant of everyone left of mainstream Democrats.

It destroyed many peoples' lives, most of who were not at all sympathetic to Soviet-style communism.

Similar to your example, we could also argue that McCarthy was indeed effective at preventing Soviet-style communism in America (since the US still has free speech and there has not been another holocaust). But in both cases we don't have convincing evidence that suppressing speech was actually helpful.