Well. Dependant how you define threat, but people could see that change was immediate. The French Revolution ended the long duree, and the various socialist movements reenforced change.

It was clear, that the conditions of living, as well as the lack of democracy weren't made to last. Things were bound to change one way or another, and old privileges were very much in question. The people who had power and money could see very obviously that their position came under fire.

Now more concrete to your question. The Paris Commune 1871 was the first large scale communist revolution. The October Revolution was the second. The Revolution in Germany in 1918 was the third strike. You had Soviets in Austria, civil war in Finland and Hungary became communist for a short time among other things.

Now the fear was somewhat founded in reality. Revolutions took place, and could spread very fast. Socialism was young, and it was a very dynamic movement at the time, and it threatened old privilege. Not only through revolution, but by legal change.

But the threat for real worldwide revolution was overblown, as there never was "Communism". The ideologies in the various countries was different very often, the stance on revolution was not monolothic (The Revolution in Germany basically failed because SDP didn't want it).

The end of World War 1 marked a very revolutionary period, it was the biggest war ever, drained the populations and the goals weren't important for the average guy. It was a slaughter for nationalist and imperialist gains. This led to very much resentment, anger and revolutionary fervor. But this didn't last long. With the defeat of the German Revolution this period ended. The only country were the revolution won was Russia, and Russia after the war, and Russia was economically fucked after it. With Trotsky also the wish for worldwide revolution died, and Stalin isolated the Soviet Union very much. If the revolution in Germany had succeeded, history would look a whole lot different. But this didn't happen.

While the Revolution didn't win, workers still got some economic demands through, working conditions, payment, social security etc. changed. This happens more or less everywhere in Western Europe, at latest with the period after the Second World War.

Addendum: The Soviet Union was used in Western Europe as a boogeyman to supress worker movements. Every strike etc. was used to make connections to the Soviet Union, to discredit demands for eg. social security.

Simple. Communism takes power from the aristocracy and powerful and puts workers in charge.

It would have been a massive power shift in the west and there is no way they were going to let that happen.