I believe that Kevin Drum has the history correct on how the TV networks adopted red and blue for their electoral college maps -- it was just dumb luck that those colors happened to fall that way in 2000, and then...well, he says that it was "the famous electoral map showing blue coasts and a vast swath of red everywhere else made its debut. This prompted everyone to start talking about red states and blue states, and ever since then it's stuck." I'd put less emphasis on the distribution of where the electoral votes were, and more on the oddity that unlike normal years, the electoral college maps stayed on our screens for weeks in November 2000, thereby sealing those colors. My memory is also that at least one network (CBS?) had the colors the other way around in 2000. He's certainly correct that the fixed colors date to 2000, no earlier.
The other thing I'd say is that had it been the other way around, I'm fairly positive that Democrats would have objected to being the red party, and the networks might well have obliged them. So it was far more likely that both parties would accept GOP Red, Dem Blue.