Hi,
That's a nice one. It looks to be a fraternal organization hat, as you suspected. The gold gilt stamped letters look like they might match the hand written initials. Probably made of a silk plush over a hard base. I do not know which organization it represents, but the shape is fairly standard. It does not look to be Masonic, it is a bit different than the ones I have seen. Most have white plumes, and your black plume may indicate something as well. Dating can be difficult (for me, not my specialty) as the hats themselves changed little from the late Victorian to the mid 20th century. A 1920s date could be right. As I said its a nice one.
It could be a theatrical piece too, but those were usually the same hats, purchased from a hatter who specialized in fraternal and military hats. A theatrical milliner would find it easier to purchase and adapt the styles than to make these, and it looks so well made.
You might do an online search for fraternal organization head wear and see what matches.