Joe,
It wouldn't surprise me
There have been various reasons for different size membership badge, such as for males & females, different ranking within the organisation (as Dave suggests), and to differentiate between actual paid up members of a group & their supporters, as with the size differerence of Steirischer Heimatbund & Kärntner Volksbund badges.
As an added bit of info, the organisation lasted with a slight name change, into the 1950's at least, as shown by these badges offered by Hüsken....
Don
