The Russian Revolution of 1905 deposes the Tsar and replaces him with a democratically elected President. They subsequently leave the Triple Alliance, feeling that it was a bad idea that would eventually force them into a nasty war. Over the next few decades, they gradually democratize and liberalize.
The US joins of the Entente in 1911 under Taft, and is thus dragged into the Great War in 1914, and the American Police State is established that much earlier, and lasts much longer. While nominally a member of the Triple Entente, the United States' involvement is extremely tokenistic. The war drags on for seven years with Germany having to fight a war on only one front, until it finally ends in a victory for the Entente.
However, with the racial segregation and brutal repression under the American Police State, revolutionary fervor finally boils over, and a loose alliance of socialists and other leftist radicals seize control of the USA in a bloody coup in 1921, shortly after Woodrow Wilson's election to a third term, and shortly before the end of the Great War. The military avoided involvement for a variety of reasons - failure to be payed their dues for the war, the war itself, sympathy for the repressed socialists, and dislike of Woodrow Wilson seeking a third term. Only a relatively small number of troops attempted to "liberate" the United States, and a similar number fought them off.
How plausible is this?
Note that when I say "the American Police State," I refer to the policies of informal, formal and often violent suppression of anti-war Americans (particularly the socialists), the growth of racial segregation and the Sedition Act of 1918, which were enacted by Woodrow Wilson.