Wouldn't a hare/rabbit mix felt get wonky if it got wet?
Max you sometimes read a little too much into fur type/blends/mixes. First of all, Pilgrim brand hats are the name of the hat carried by Sears Dept. Stores back in the day. The same as J. C. Penney Marathon hats, these were contract (jobbers) hats. There is some information around the lounge that says Lee was the mfg. of many of the hats carried by Sears and Penneys.
Fur blends from the day were proprietary and the secrets of the blends were safely guarded. Hare/rabbit, hare, rabbit and beaver hats and the varying blends have been around for some time. There's information about that suggests wild hare, next to beaver is the best material for hat fur. See Akubra, though they now import rabbit fur for their hats. As far as the finish of the hat, regardless of the material used, would depend on the maker and the one finishing the surface of the hat. No well made hat is going to get "wonky" when wet, at least none of mine have. Fully soaked and crumpled in a corner to dry, yeah that'll make one wonky. If I remember correctly Lee was one to really push how effective their hats were at shedding water.