I have recently played my first game of Scythe with a roommate. The two player variant. We came across a question we could not discover the answer to.
If through events/actions etc your popularity gets to 0(zero) are you allowed to continue taking actions that result in negative popularity? For instance, are you allowed to attack a hex with a worker on it and send it home, even though your popularity can't go down anymore?
You're asking two separate questions. You may take actions that result in negative popularity (although your tracker can't drop below zero), but you may not take any actions that "cost" popularity.
In your example, yes, you may attack a hex with a worker on it because the drop in popularity is a result of your action. Your popularity would remain at zero.
However, if you revealed an encounter card that required you to lose popularity to get x resources, you would not be able to take that action as you can't pay the "cost" to perform it.