Yes, Odd Fellows wear a fez. But not every Odd Fellows does and only certain ones can.
It’s important to note that besides the “official” Independent Order of Odd Fellows guidelines (see below) which extend to Encampments and Grand Encampments, there are two appendant (or “side) degrees/organizations which are recognized in some form by the IOOF but not embraced in a subordinate or officially fraternal way: A.M.O.S. (the Ancient Mystic Order of Samaritans) and the Noble Order of Muscovites. Both of these groups embrace the use of the fez and have their own stylings and rules for use; A.M.O.S. takes its theme from the same part of the world as the Shriners (namely old Egypt or Sumeria or somewhere “mystical” and ancient) and Muscovites are obviously Moscow-related in some way.
Without the need to rewrite the great content and images of fezzes in their museums, two websites have pictures and the history of both A.M.O.S. and Muscovites and worth a read. The first of these is FezMuseum.com which also contains fezzes from over a dozen fraternal orders with the link zeroing in the AMOS/Muscovites page and it’s really a great account of the different appendant groups that are still around and those that have been lost to the sands of time. The second site that has a lot of information (although not quite as many examples of fezzes, but also a fine recounting of the history of fezzes as they pertain to Odd Fellows lodges (no longer in use), encampments, and appendant bodies; it’s worth noting that this second site has a particular Odd Fellow wear a fez because it’s black and orange for a Lady Muscovite!
Odd Fellows Wear a Fez in Encampment
(Prepared by Co-Founder Peter V. Sellars, PGP/PGM and Written at the Request of the California Grand Encampment; Adopted 2008.)
There are several organizations who wear the fez. Shriners are probably the most noticeable; however, the Independent Order of Odd Fellows have used the fez in its organization for over a century. Over the years within the organization, the Odd Fellows lodges, the Junior Lodges, Ancient Mystic Order of Samaritans (A.M.O.S.) and Zuannas, the Encampment and the Ladies Auxiliary have all wore the fez. Today the encampment branch of the Order primarily retains use of the fez, where the others no longer use them.
Some lodges used to wear fezzes that were red or white in color or tri-color red, white and blue (all of which are in the San Francisco Odd Fellows Museum); there were blue fezzes used in some Junior Lodges (also in the San Francisco Odd Fellows Museum); the A.M.O.S. and Zuannas also wore fezzes. The encampments have used variations of the color purple. Today, several encampments still retain the use of the fez. The history of the fez is prominent in the Independent Order of Odd Fellows.
Source: San Francisco Odd Fellows Museum. The aforementioned is factual and not supposition.