This article is from the The Religious Society of Friends FAQ, by Marc Mengel firstname.lastname@example.org with numerous contributions by others.
Many people, are under the impression that Quakers have rules
about clothing, hats, bonnets, etc. similar to the standards
among the Amish, the Old Order Mennonites, and certain Orthodox
Jewish sects. One explanation for this confusion is the image
on the Quaker Oats(tm) logo (See (1.4) Oatmeal, Motor Oil...);
another is the traditional refusal of Friends to rise or doff
their hats to figures considered to be in authority.
(See (5.2) Authority)
While most Friends do dress less ostentatiously than the average,
this is more a reflection of the overall Quaker emphasis on the
inner spirit rather than outward appearances, not any sort of
enforced restriction on clothing.