[Clipper]

This does seem legal, but there is a way to stop any of them from doing it. Discard your Race, Class or Hireling to cover up Divine Intervention. You can do any of these actions at any time, even when it's not your turn. If you can find some other legal way to discard a Door card (e.g., playing a non-continuing Curse or a theft attempt if you're a Thief), that's good too.

And Bampop, even if the Clerics are choosing to discard Doors, they can manage it. A ruling the other day made it clear that Divine Intervention would be discarded at the same time as the discard cost the Cleric pays, and given it's the Cleric's turn, they can put Divine Intervention on top of the discards.