The fear of radicalism that happened after WWI is typically known as the "red scare" or sometimes the "first red scare." During this time, Americans were worried about the growth in radical ideas, especially among immigrants and workers. There were three main causes of this fear.
First, there was the fact that Russia had become communist and was overtly talking about spreading its revolution abroad. This made Americans fear that their country would be a target for communists.
Second, there was the large influx of immigrants, some of whom were radical, in the late 1800s and early 1900s. Americans felt that there were large numbers of radicals among the immigrants and that American ideals were in danger.
Finally, there were major strikes in many US cities in 1919. These strikes helped to convince many Americans that the labor movement was filled with these radical immigrants who were going to topple the US system.
For these reasons, a fear of radicalism arose in the US after WWI.