Why would americans might have felt threatened by foreign ideas?

Simply because they were different

They did not fit with american government and society

Socialist and anarchists were unpatriotic (opposed the war)

Anarchists believed in violence and had targeted americans with bombs

After the war, americans were distrustful of foreigners and their ideas

American people generally believe that the ideals of the founding fathers are the best ideals because of things such as democracy, unalienable rights, the constitution with its amendments, and similar things. Whenever someone would show up who would claim otherwise that person would be accused of being a traitor or a spy or something similar. This was especially important during the red scare when they tried to fight communists in the US more than anything else.