Reframe the conflict from "whose priority wins" to "what outcome are we all trying to achieve for the user?"
Best answers show facilitation skills: bringing all parties together, reframing the discussion around user outcomes rather than departmental goals, finding creative solutions that partially satisfy all parties, and getting genuine buy-in rather than forced compliance.
Core PM responsibility. Watch for whether the candidate positions themselves as a neutral facilitator or takes sides. Best PMs find the underlying user need that unites competing priorities.