Notice the temporary change in choice of buddies. Random textures will be applied on a later update, or rather the choice of giving your buddy a new skin.
Trivia: Buddies only have one texture. Sheep however can be dyed by using any dye. But due to the buddy’s unstable life form, it will assimilate the color, but give another result, resulting in your Sheep buddy’s fleece color going wild, and giving him a random color every time you try tio dye him. This also means you might see colors normal sheep would never have !