This is an odd item. The imagery sure looks to be Beistle but there is no evidence they ever designed a band hat with that imagery. (Now, records from that time, early 1920s, are not as complete as they could be, but in consulting the many sources that do exist, I've never seen one with that design.) Interestingly, Beistle at that time took pains to mark everything with at least a Made in U.S.A. mark, but this item does not appear to have even that kind of minimal marking. The grade of the cardboard and the way the honeycomb is designed look absolutely "right" for the assumed time period. I feel this is likely an example of a rogue firm simply exploiting Beistle's artwork and putting out an unlicensed item. Although I don't know that for sure, what I do know is that the design of the item is quite cool. I like how the JOLs pop against the white background.
07/23 Update: This sold for a very respectable $100.99!