Importantly, Wilson was on the “internationalist progressive” side of the progressive split just before the turn of the century. The “nationalist progressive” leader was Teddy Roosevelt.
Conservatives did not back either side, though leaned towards nationalism.
The split happened at the same time in Europe, with the nationalist progressives eventually backing the Nazis and the internationalist progressives backing the communists.
Yet once again, conservatives wanted nothing to do with either side, but also leaned towards nationalism.
The real radicals of the time were revolutionary anarchists, many of whom came as immigrants from the protracted Italian unification and the Balkans. Since they could not easily obtain guns, their weapons of choice were bombs, much like the Russian Bolsheviks.
See the Hayek quote on my profile page. 2 paragraphs, 3rd quote down. Summarizes the European aspect of that very well.