If possible, at least one Worker must move up this turn.
The general case of this question is whether a player may, by actions taken before their worker moves, subvert or otherwise work around this requirement.
For example, Charon's power states:
Before your Worker moves, you may force a neighboring opponent Worker to the space directly on the other side of your Worker, if that space is unoccupied.
This presents two interesting and somewhat parallel cases:
1. I (Charon) have a worker who may move up into a single square, or I can flip my opponent (Perspehone)'s worker into that higher square, thus removing any possible upward moves and freeing my worker to move about the board as it pleases. It was possible for me to move up, but then before my move I acted to make it impossible. Is this a legal move?
2. One of my (Charon's) workers is able to move up and is not adjacent to any of Persephone's workers. The other of my workers is adjacent to one of Persephone's workers and has a clear path to flip that worker over. I choose to flip, and then must move the worker I flipped with (per Charon's rule). Thus, it was possible for me to move up, but through Charon's power I made it not possible.
The ruling my opponents and I came up with in the moment was that we could use Charon's power to nullify (temporarily) Persephone's power, mostly because that made for a more interesting game. But we are curious as to whether this interpretation makes sense and is consistent with other rulings.