Unmarried daughters wear white in Gilead's dress code. These daughters are the natural or adopted children of the ruling class, and their white clothing marks them as young women who have not yet entered marriage.
Marriage for daughters is not presented as a private choice. Gilead arranges their marriages, and the girls' status is tied to the ruling elite's effort to preserve family hierarchy and social control. The white clothing therefore signifies both youth and their position within the privileged class of Gilead's households.
This detail is easy to mix up with the colors assigned to other female groups. Wives wear blue, Handmaids wear red, and Marthas wear green. White is specifically associated with daughters before marriage; it is not the standard color for Handmaids or Wives. The narrator's daughter is shown in the historical photograph wearing a long white dress, reinforcing the rule.