I think the Russians didn't adopt the Gregorian calendar, which we did in 1752, until the revolution in 1917. The difference was eleven days.
You were definitely on the right track, jrvass. I emailed the link to Moe's draft card to Joan Maurer, to see if she had ever seen it before. I usually wouldn't post something like this, but I thought it would add some further clarifications. Here is part of the response she sent me:
"Moe's mother bought the Chatham farm so the boys could work on the farm and not be drafted so none of the boys went to war. ...Because the Jewish calendar is not that accurate, Moe celebrated June 30th until he went to get his passport to go to England in 1939. That's when he realized he was celebrating the wrong date.
Back to work.
JOAN"
...
And if I'm not mistaken, I believe the same thing happened to Larry when he went to get his passport for their '39 UK tour. I remember reading it in "Stooge in the Middle," the book that Larry's brother wrote. ...Apparently, he found out that his actual birth date was really
September 5th, and that he had been celebrating it on October 5th the whole time. However, he still chose to 'keep' his birthday on October 5th.