Units can only equip one Diana’s Sigil. They can have both a Diana’s Sigil and the flag equipped at the same time. If a unit moves onto a chip it cannot equip, the chip simply stays on its hex, face up, until another unit that can equip it moves onto it.
Nothing changes in the rival priority list, so they still mark unequipped arena chips even if they cannot equip them, in order to block the player from getting them.