Trotsky's vision of permanent revolution would lead him to try to foster communist terrorist movements across Eastern Europe. That gives fascism an even bigger shot in the arm than it got historically, while he would not have been much different than Stalin in terms of the paranoid butchery. In fact perhaps even worse given Trotsky was a very, very latecomer Bolshevik and would have been more insecure in power than Stalin was because he wasn't just a latecomer Bolshevik, he's also Jewish.
Hitler rises to power more decisively IOTL when his "Judaeo-Bolshevik" lies have even more plausibility. It depends on who, what, and when Trotsky purges and whether or not he'd try a Molotov-Ribbentrop Pact to say what happens after that.