Engageante sleeves were made from…

…fine lace, linen, cotton lawn, cambric, or Broderie Anglaise (cotton with holes that have been embroidered around), were easy to remove and launder.

That’s why they were white.  (Plus after romping with a wet dog, they could be dried quickly).

(Photo: Museum quality 1860’s engageantes not on a person with extensive embroidery on white cotton lawn)