After installing the Unofficial Skyrim Patch, this combination is no longer possible. If I equip the one and then the other, the first gets unequipped like they are not compatible.
I can only guess the authors of the mod introduced this change as a reaction to this Skyrim bug:
[PC]  While wearing the robes, Dragon Priest masks (such as Morokei and the Wooden Mask) might make the player's head invisible, to solve this, drop the robes and pick them up, or unequip the mask.
How can I make this combination possible without having to give up on the fixes introduced by the Unofficial Skyrim Patch?