Reagan was an FDR Democrat, a bigtime new dealer.
So what. Reagan even called himself a liberal Democrat in the 1930`s. With the outbreak of WWII, that began to change. By 1952, Reagan voted for Eisenehower and the rest is history.
OTOH, Rudy Giuliani was born a liberal, and will die a liberal. He can call himself a Republican. As with most conservatives, he won't ever get my vote. Not now, not ever!
As evidenced by the growth of social welfare programs while he was governor.