The general trend that is visible is that Islamic states tend to prefer green, Communist or former Communist countries prefer red, European nations prefer burgundy and the rest have mostly gone with shades of blue.
Minor bit of trivia: European Union countries[0], with a few exceptions, all use a standardized passport format[1]. The burgundy red color is specified. (This was one of the reasons given by the "Leave" campaign in the run up to the Brexit vote, that the United Kingdom would be able to return to a blue cover color.)
https://en.wikipedia.org/wiki/Passport