Firstly, several countries did have similar worries about communist spies, revolutionaries and militias. And in fact, this was at times true: far-left revolutionaries and terrorists were actually a problem in some western European countries, for example in Germany the Red Army Faction (better known as the Baader-Meinhof gang) and Revolutionary Cells. Not to mention left-wing/nationalist terrorists like the IRA and ETA.

However, while intelligence officers did search out left-wing agitators, and groups like MI5 did keep tabs on prominent left-wing activists, intellectuals and celebrities, there was not the same visceral dislike of Socialism.

Why? I'd argue that the main reason is simply that many European countries were ruled by Socialists, or their watered-down version, the Social Democrats. Several countries had small Communist parties in parliament, or even occasionally in coalition governments.

Although most have given up on mass nationalisation, most European states still have prominent Socialist or Social Democrat parties today. For example, the British Labour party, the Sozialdemokratische Partei Deutschlands, Parti socialiste of France (which is currently in government), Partido Socialista Obrero Español, etc. While in America the main seperation that developed was between Conservatives and Liberals, in Europe the main political divide has been between Conservatives and Socialists (both of whom have been influenced by Liberalism) with Liberals generally taking the part of third party (for example, the British Liberal Democrats, German Free Democrats, etc). Most of these Socialist parties are, or at least used to be, members of the Socialist International. Until the 90s, the Party of European Socialists was almost always the largest Party in the European Parliament.

So, of course, these countries were much more sympathetic to Socialism. It's hard to view Socialism as anti-British when Prime Minister Clement Attlee is nationalising industry and the health service, while in America it was much easier to view Socialism as anti-American.

Now, it should be said that many of these Socialist parties were explicitly anti-Communist, and were supporters of NATO, as they considered Communist governments to be dictatorships. But they were still more sympathetic to left-wing academics and celebrities.

I would also argue that anti-socialism was a crucial element of American political ideology (of the elites and of the right wing) long before the 1950s.

Anti-union propaganda in the 1920s and earlier was usually framed around the claim that (somehow) unions were a step towards socialism--and thus, un-American.

For instance, the attack on the Bonus Army--US Army veterans from the First World War--by the US Army in 1932 was justified primarily by the claim that there were "communists" in the encampment.

But you can see this also in the massive reaction to the Haymarket Riot (1886), which set in motion widespread attacks on labor organizers as socialists/anarchists.

I might even argue that, in start contrast to Europe, anti-socialism played a much greater role in American political culture than socialism itself. But other historians might argue this.

Overall, the US had a Red Scare in the '50s because socialists had been demonized in American politics for the previous 80 years.

I can't speak for the rest of Western Europe, but the right wing in West Germany did not need a Red Scare to convince the populace that Communism was bad.

Even without the memories of the Soviet Union and the expulsions from the Western Bloc and the clear superiority of living in West Germany to the East, and the days of the Reds in the Weimar Republic before that, there was a strong desire for peace, quiet, and stability that did not favor the Communists. The people just didn't want to think all that much about politics. Adenauer got elected on the slogan "No Experiments".

This only changed when the postwar generation went to college.