European political parties all tend to support some socialist ideas (such as universal health care, welfare systems) to a much greater extent than the two US parties do. The fact that one US party has become practically rabid in it's opposition to even the mildest forms of social politics just makes this seem far more extreme.
The US also has a historical tendency to equate socialism with communism. The two are completely different and no mainstream European party with a hope of gaining power supports communism.
The US is as close to a pure capitalist system as is possible. It has always been driven by a model without socialist elements. This is culturally embedded in the US psyche. The Cold War meant that any socialist concepts were equated to communism, and this has colored US thinking since.
Europe, which developed from the fall of European monarchies, already evolved some socialist principles even before the monarchies fell (look at e.g. Germany pre-WW1). Socialists in Europe were never quite equated to Communists. Socialism in Europe is seen as more related to the struggle for social justice and workers rights. Rather than been seen as some sort of foot-in-the-door for communists, it is seen as a cornerstone of the development of political parties that supported union rights, workers rights, freedom of political action, welfare and universal health care.
The fact that US politics is extremely polarized and has evolved to a two party system driven by what, by European standards, are simplistic black-and-white principles, means there is practically no middle ground in the US. Workers in the US never united in parties like the Labor Party (in the UK and Ireland). US politics has become confrontational and the label "socialism" is avoided by both sides. In Europe politics is not as confrontational - collation governments are common. working politics, even between superficially opposing groups, means a lot of middle ground compromise politics is done to keep things working.
So the atmosphere of European politics combined with the less-negative view of socialism means socialist politics are not seen negatively. The benefits are tangible and real.
In the US, socialist policies have never really been tried. There is a confrontational bi-party system that is deeply entrenched and no movement that challenges this. With no experience of socialist policies there is only the negatives of communism (and failed communism at that) to gives a false impression of negativity to socialism.