Why is that unusual? Even in Imperial Germany(probably a more antisemitic place than Austria-Hungary), there were field rabbis during World War I. The majority Jewish unit is new to me though, thanks for that.Did you know that the KuK Army had military rabbis?
Because HoI3 has a very underdeveloped politics system. In DH, money is very important for research and spying, dissent can be potentially crippling and takes months or even years of valuable IC in consumer goods to clear out, and the event system is excellent for the non-war interactions between nations that Kaiserreich truly shines at. HoI3 is much more combat-focused.