Why must they be white?
Something to do with a special kind of paint used - strange but true (I am reliably informed!). Applies to both the RR and GE engines.
See Boeing's impression of the BA 787:
BA 787
Compared to their impression of the BA 777-300:
BA 777-300
Other Boeing 787 liveries where the engine is not usually white include:
S7 Airlines:
S7 787 (usually snot green)
First Choice:
First Choice 787 (usually cyan)
Here is the Virgin artists impression:
Virgin 787
I think there is a lot of "artists licence" with the Virgin one - if the fuselage remains the current silver then the contrast against white engines will be very stark.