It kind of started back in 1976 when color came to television and the election results were put on a color-coded map that was readily viewable by all. Color-coded maps were nothing new, but not really common before color television and four-color newspapers became the norm. And it wasn’t until 2000 (yes, a mere fifteen years ago!) that “Red = Republican, Blue = Democrat” thing came about as an attempt to get all the media outlets to use a consistent color scheme.
I find it is of useful as the geography matches the cultural borders.
Most of the states that lean Republican and show up as red on electoral maps are full of people a bit more Christian than us heathens. Conversely, all of the states where women and minorities are not specifically discriminated against by law (and, in fact, have legal protections) tend to be in one of two places; the Northeast and the West coast.
It’s a little more complex in that a lot of Southerners are ideologically aligned with the Midwest but have a distinct cultural identity, while the same is true in that the West coast is quite different from New England, but the difference between a Seattlite and a Vermonter is relatively minor compared to the differences from Texans, Georgians, Iowans, or people from other “red” states. Those from “blue” states are not terribly different from many Canadians or Western Europeans while those from Dixie and the Heartland are from a different country that happens to be ruled (to the extent that they obey) from the US capital.
You could separate the US along party lines and only have three pieces, two of which used to actually be independent sovereign nations for about four years a while back. Because SO many things vary in ways that coincide with the red/blue you see on the maps, the dichotomy between red and blue is quite relevant so long as we have that sort of “two nations ruled from one capital” thing happening.