However they still functioned as a monarchy, so in game they would best be represented by a monarchy with full narrowminded (and/or full theocracy in mods that have an extra slider like that).
And going by the naming conventions of states in the region, Safavid Persia would just be called Safavids rather than Persia. I assume it's called the latter because it held on to the area of Persia far longer than its immediate predecessors, and so historically they became known as a dynasty proper of Persia, rather than a temporary conqueror. If other states can hold onto the region and have their center of power there, I see no reason why they shouldn't be allowed to "form" Persia, and as such, on top of other reasons, I don't see why Persia should by default appear as a theocracy.