At this point, we're going to give up. We're not going to find that Jewish Olympic medalist in tug-of-war.
Yes, tug-of-war. Team rope pull, if you will. In the Olympics. Contested every iteration from 1900 to 1920. Won twice by the Brits, once by Americans, once by Swedes and once by a mixed team of Swedes and Danes. No Jews. (Perhaps some hidden Jews?)
Oh, we had some hopes about American medalists Max Braun and Harry Jacobs, but no confirmation of their potential Jewishness exists. So, let's talk about the 1912 competition, when hometown Sweden won gold against Great Britain. No other teams competed.
Austria, Bohemia, and Luxembourg also entered, but neither showed up. (Like Luxembourg had a chance!) The entire competition was reduced to a best-of-three final. Sweden won the first pull, but the second could not find a winner. The Brits got tired and sat down. Well, as any tug-of-war aficionado knows, you can't sit down! Sweden was declared champion.
That Swedish team was represented by the Stockholm Police (although it somehow included one fisherman). So, yes, while the handsomely-mustached Adolf Bergman did have a definitely cromulent Jewish name (even "Adolf"; that was obviously fine back in the day), there is absolutely nothing to suggest to suggest that he was Jewish.
Apparently, Bergman also played the violin? What a renaissance man! Could it be?...
Nah. We give up.