I haven't come across any evidence of actual rules related to bedding colors. The main constraints seem to be physical conditions, laundry service, and personal tastes.
Physical conditions - Many soldiers are living in environments where everything gets very dirty. We never send white.
Laundry service - the quality of the laundry service varies, some seem to be pretty bad, so any thing really nice is likely to get treated badly. Also, I have seen a few references to services that don't accept anything red, I forget why.
Personal tastes - A lot of the guys prefer conservative colors. My impression is that most of the women prefer anything but. The occasional exception seems to be females (esp marines) living in harsh combat conditions who feels the need to be seen as "one of the guys," especially if the female is the only one or one of a very few females in her unit.
Generally, I don't send any "creative" bedding out blind...that is, not without having had prior communication with the contact that gives me some idea of their circumstances and preferences.