At the risk of explaining a joke into the ground your comment has more than one reference. The UK's two main parties have their colors flipped. Labour's color is red.
Dems were red for longer on political maps than they have been blue. It was an odd quirk of CNN's maps in the 2000 election that made Democratic Party = Blue and Republican Party = Red in our minds. The fact that the map was everywhere for weeks while Florida was decided meant that it stuck instead of returning to what it had previously been for decades.
In 2000, the NY Times arbitrarily went with Red for Republicans because the first letter matched. This was the first time they printed color maps for an election. Everyone else kinda just went along with what the NY Times was doing that year.
And yeah, like you say CNN was showing that map a lot in 2000 and once people started saying "red state" and "blue state" it kinda stuck.