I’m going out on a limb here, but I thought the Kotzker might be refering to the “donkey” as in Yissoschor, who can only tread the path of Torah. The “people” are the Zevulins of the world, but need to choose a side, meaning are they going to defer to the Yissoschors, or are they going to manipulate them?
Or, choosing a side might mean, as a Zevulin, you need to choose a profession, but make sure you choose wisely.
Thoughts?
(I was also mulling over the donkey of Pinchas Ben Yair, but could not delevop a trail, so I’ll go with the Yisoschor track)