A bit of quick research indicates that is not at all true. Since 1913 most were Yankee blue-bloods. Eugene Meyer was probably the first Jew in the position before Alan Greenspan.
I believe William McChesney Martin, who was Fed Chair for 20 years from 1950-70 even studied at a Lutheran Seminary.
Fewer than one-third of the 16 Fed chairs have been Jewish. I wasn't a math major but I still believe 31.25% is still less than 100%.