How is this a political allegory?

All I can come up with is how desperate people (Rath) are drawn to powerful, charismatic personalities (Lola) who will use and ruin them. Then consider the time and place, and the political party gaining momentum.

I mean, what point don't you understand? Though don't expect a 'modern' straightforward politically correct and clearly pinpointing allegory.
(That's why I love mostly old movies: for their subtlety!)

Just ask yourself about the social classes, and ask yourself, who in the whole plot is at ease, in a positive state of mind, with perspectives? This isn't Rath, who lingers in a ritualistic existence, with his maid. Lonely, with little dedication to teach the pupils. The pupils, mostly disinterested, or a boot-licker, wasting their time in a cabaret. The whole troop, a sad clown (!), with the troop as last resort, a boss, who panders to the honorable professor, an old drunkard 'captain', a bored audience who try to get a glance at women's legs (something their their wives probably withheld), and on top a singer, who is more of a visual prostitute. She has a heart, she loves the bird (hers is still alive), she has the puppet, and mostly loves to be adored.
Neither has the chance to realize their aspirations, everyone seems stuck in a social context, be it high or low, little to no chance to meet people from another classes constructively.
Josef von Sternberg offers us a wonderful setting and cinematography showing exactly that: how everyone lives in their own little prison cell. The cells are there, clearly marked, and yet invisible.