It is said that in pre-war Frankfort, they even had a white carpet in the synagogue on these days.
The preference for white may be an act of historical identification inspired by the white robes worn by the high priest in the Temple at the culmination of the atonement ceremonies.
The advantage of white at a season that focusses on forgiveness is that it is a clean colour; Isaiah said, “Though your sins be as scarlet, they shall be white as snow” (Isa. 1:18).
Others say that white represents our feeling of confidence as we face the Divine judge, reminds us of the angels in their spiritual exaltation, and, because it is the colour of shrouds, makes us feel that this is a life-and-death moment.
Red, by way of contrast, is the colour of blood and reminds us that, as Isaiah also says, human hands are often stained with blood (Isa. 1:15), if not literally then metaphorically, when we consider the harm we do to other people.