To direct you to a couple older answers I've written:

First this one about the McCarthy Era and the "Red Scare" years of the 1940s and 1950s: while there was a general American fear of communists and communism, much of it was very specifically focused on Communist Party members and sympathizers, and Soviet spies in general. It's worth being clear here that while ideology wasn't unimportant, specifically what the fear was was that certain organizations like, for example, labor unions, were being operated as "fronts" by Communist Party members who in turn were acting on behalf of the Soviet government, whether directly as intelligence assets or more indirectly through political coordination through such bodies as Cominform.

Second I'd point to this answer I wrote about US treatment of other communist countries during the Cold War years. While the US would definitely have considered itself "anticommunist" in broad brush-strokes, its actual foreign policy was much more focused on Soviet containment or countering Soviet military and foreign policy advances. To this end the US was perfectly fine providing massive material aid and decently warm diplomatic ties to communist states that were on bad terms with the Soviets or with Soviet allies, and Yugoslavia, the People's Republic of China, Romania, and Somalia all were recipients of this American goodwill and material aid when their interests aligned with US interests.

But if we're speaking in slightly broader terms - and here I am assuming when we're talking about "Western" countries we mostly mean North America, Northern and Western Europe, and Australia and New Zealand (I think Japan maybe but it's probably worth treating as a separate thing): much of the initial hostility to the Bolsheviks and Soviet experiment came from an initial Bolshevik commitment to world revolution. Namely - according to Marx's own understanding of history, the workers' revolution should occur in the most advanced capitalist economies, which by his estimation were Britain and Germany. Russia was not supposed to be where socialism gained a hold, as even in 1917 it was a massively agrarian peasant society. Lenin and company sincerely struggled to explain this, and to sum up their thoughts the idea was that Russia was the "weakest link" in the capitalist chain, and that Bolshevik success there would lead to imminent revolution among the workers in the rest of Europe as the First World War ground down the capitalist order.

To this end, the Bolsheviks organized a body known as the Communist International, or Comintern, in early 1919. This was chaired by Russian Bolshevik Grigory Zinoviev and was to be a successor to the Socialist 'Second International", and most of the member parties were from the more radical leftist side of existing socialist parties. As a whole, European socialist parties had tended to support their respective countries' war efforts in the First World War, and the individuals and factions who disagreed with this tended to gravitate towards the Bolshevik position, ie that the war itself was just a conflict between imperialist capitalist states, and that the ideal outcome was a universal workers' revolution. Most of these groups would become Communist Parties in their own right - the German Spartakist League was in the process of founding the Communist Party of Germany, for exampe. Italy was unique in that the majority of its Socialist party, the PSI, threw its support behind the Bolsheviks and the Comintern.