The way I see it, you take the conflicts that already exist between allied colors and exaggerate them, and do the same for commonalities between former enemy colors.
GW: Same as before. Shared love of harmony and belonging.
WU: Same as before. Shared love of building a better society.
UB: Now enemy colors. U thinks B is small-minded and overly materialistic. B thinks U has its head in the clouds.
BR: Same as before. Shared desire to do what they want, when they want.
RG: Now enemy colors. R feels G is passive and uncaring about what is going on. G pities R and sees the color as lost and unwilling to find its place.
WB: Same as before. W sees B as selfish and parasitic. B sees W as delusional and unwilling to recognize human nature.
BG: Now ally colors based on a shared understanding that the world will always be how it is now. The only difference is B wants to exploit that world while G wants to coexist with it.
UR: Now ally colors based on a shared love for change and pushing boundaries. The only disagreement is that U focuses on long-term goals, while R is focused on short-term goals.
RW: Same as before. W sees R as destructive and chaotic, R sees W as stifling and static to its personal freedom.
GU: Same as before. G sees U as disrupting the natural order. U sees G as stopping progress.