Iranian Mobeds don't seem quite as exclusive as Parsis.
There is a short answer to this and a very long debate, but I'll take the middle road and give you some background perspective to the relationship between the Zoroastrian communities in India and Iran since they separated 1300 years ago.
Till around the 15th century, the Iranian priesthood were the seniors, and Parsis were the junior priests. Iranian priests set the path which the Parsi community in India followed.
From the 15th to the 18th century things became really tough for the Priests in Iran. They realized that to survive both the remaining atash and mobed families in Iran would now need to be moved to India.
That is why now of the 9 main Atash Behram fires, 8 are in India and only one survives in Yezd.
Of the 8 in India, 7 were moved between the 16th and 18th centuries to Bombay. The original one we came with surviving in Udvada, as the Iran Shah.
The treatise of the Parsis in India was written by an Indian head priest (Dastur) in the 16th century. Called the Qissa-i-Sanjan.
Between the 15th and the 18th centuries there were a series of 19 theological epistles, called Rivayats, written between our priests in Iran and India, on matters of the religion and rituals and customs, as things wound up in Iran and the senior arm moved to India.
the Indian clergy now is the head clergy of Zoroastrians worldwide. And the mobeds in Iran take their direction from our Dasturs. The senior Vada Dasturji of Udvada being somewhat equivalent to the Pope. It usually being a hereditary position shared between the 4 main Dastur families that migrated to India 1300 years ago (all Indian dasturs, including me, trace our lineage to those 4 clans).
Mobeds in Iran know well who practising Zoroastrians are, even if they live as Muslims there.
Apostasy is punishable by death in Iran.
From what we are hearing now, even the suspicion of being Zoroastrian is leading to the authorities sealing and taking over properties of Iranians. Its not a good situation, and things are slowly coming to a head there ....
Either way, Indian Parsi priesthood is firmly against conversion.
Some senior priests are beginning to speak about reversion of Persian Iranian Muslims elsewhere in the world.
Priests outside India are way more open to that.
Priests in Iran cannot do anything. They are in survival mode. I meet many of them here and elsewhere regularly. Though internet is very dicey for them ...
All the Kurdish converts are being converted by Indian Parsi priests. And some Iranian expat priests. And there are many Kurds who are being trained in the rituals. But can never become priests unless the direct lineage to ancient Magi laws of the faith are amended or twisted in some way.
The risk here as many Iranians like
@Cthulhu will tell you, and I agree with him, is of Kurds breaking away when they have something of a critical mass and starting another sect of Zoroastrianism that is at loggerheads with the Persian one.
Something like your Sunnis and Shias.
Its going to be a fine balance as we drive forward for our homeland ...
Does that answer your doubt?