The Republican Party has been the more conservative party for something like 150 years now.
Just go read the umpteen posts by North Carolina Yankee on the subject.
Or are you like your fellow D-IA avatar HenryWallaceVP and believe in muh party switching?
SNCY is someone who is right at some level but is the epitome of TLDR posting. It's not so much that Rs were conservative and Ds were liberal or vice versa. It's that you had conservatives and liberals in both parties.
It's difficult because there's no national referendum - but it would be interesting to see what would happen if there was a referendum on banning CPUSA. I wouldn't be surprised if otherwise wealthy republican areas like Bergen County had a higher % of no votes than western Kentucky (which at the time was heavily democratic voting).