Don’t be so simple-minded, that is one of the most effective lines a politician can use, it is why he delayed officially registering as a Republican, it was so he could spend more than a decade campaigning for Republicans nationally as “A Democrat for Eisenhower” and as “A Democrat for Nixon”.
It works for both parties and is very effective in reaching the other party’s voters and fence-sitters.
You really don’t see any difference between having been a Democrat in the Great Depression 1930s and WWII 1940s versus being a Democrat in the party of Obama, Hillary, and Biden and weak National Defense, abortion, gay marriage, trans, feminism, drugs, etc?
FWIW, I remember back in the 1970s, when I was in YAF, conservatives were still attacking FDR and his New Deal.