I don't entirely know a way of blocking someone from moving a card, but you could use Butler that moves a card back if those criteria aren't met.
Ie... make a "when card is in this list" and add filter for "custom fields blank", and an action of "move to x list".
EDIT: I just found this power-up (Workflows for Trello), I haven't used it so I can't really speak to it but it seems like it lets you set constraints for moving a card to a new list.
If you had to thrive a new habit during a lockdown, what would it be? Trello
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