I don't think there was any real picking involved on the part of the parties... Election maps would use red and blue, but that was a very intermittent thing to look at (once every four years for most people; voter turnout in the US was abysmally low, and who knows how many voters actually watched the results with interest). And each network would kinda randomly assign them to each party, without even agreement over which is which from one network to another. And then it finally settled into consistency in 2000.
Maybe I misunderstand your comment, but my point is they didn’t. Communism/socialism is red, and the US is blue+red. If the “left” side of US politics feel a need to distance themselves from socialism, they need to claim blue as their main color. No one is likely to mistake Republicans for communists so it’s safe for them to use red.
Another way to put the same argument is that Democrats are centrists/liberals rather than left wing/socialists, so the red used by actual left-wing parties in other countries just doesn’t fit.
Apologies, I meant to say why would Republicans pick red in that case, since they're even more anti-communist, but forgot to be specific enough in expressing that
