naw you don't have to have survived the Great Depression to be a New Dealer, and not even as a term of art but in reference to the actual FDR New Deal. The Dem party has always been pretty corrupt and capitalist friendly, but they were ostensibly a New Dealer party (albeit reluctantly after the war) until Carter - which is when the neoliberals you know and loathe today because they stole your future took over.
So most of your grandparents were at least nominally New Dealers growing up if Dem.