Stay East, Young Man

While I have no hard evidence that FDR was antisemitic (and his wife certainly wasn't), it is patently clear that there were anti-Semites in his cabinet and that these folks wielded tremendous influence. Amongst the most virulent was a guy by the name of Breckenridge Long (an assistant Secretary of State) and it was this guy specifically who pushed through those draconian immigration quotas from eastern Europe both prior to and during the war, a policy it is fair to say that led to a great deal of suffering at the hands of not just the Nazis but the Commies as well. Thankfully this policy was eventually amended as lesser bigoted individuals came to fore but you still have to wonder, the damage.