No, I think you missed the point, it’s not a comparison today and the past, but in the past.
In the 1930’s the Democrats were the party of segregationists (clearly not a left wing position), but also the party of FDR expansion of social programs (clearly a left wing position).
There is a two part explanation. First parties are coalitions, and the segregationists might or might not have been the same people pushing the social programs. Secondly the parties in the US were much less aligned on ideological grounds at that time than they are now. Today the Republican Party is almost entirely conservative and the Democratic Party liberal, but back then the parties were much more mixed.
Bismark, a far right monarchist, introduced the first universal healthcare insurance system as a result of a combination of fear of the left and christian morality. The notion that government spending is unique to the left is a modern US conceit.
In Europe a significant proportion of the right are Christian democrats of various flavours who consider some degree of state welfare to be moral duty, and/or other non-free market conservatives, to the point where the US style right are considered extremists many places.
