In the Lunar Provinces, about 26% of the total population follows the Lunar Way. The Lunar Way was introduced to the Provinces between 1330 and 1350 with the campaigns of the Conquering Daughter. Lunar colonies were established with settlers from the Heartlands – these colonies remained Lunar during the chaotic years of 1375-1460 when the Lunar Provinces were largely not under Lunar rule.
The rate of conversion in the Lunar Provinces is pretty close to historical precedents and aligns closely to the Islamic rate of conversions in Andalusia or Islamic Egypt. It is significantly faster than the rate of conversion in Islamic ruled India.
In Tarsh, almost half the Lunar population (35%) is descended from colonists from the Lunar Heartlands. This is more like the speed of the spread of Christianity from 320-420 AD. But Furthest and the Reaching Moon Temple explain much of this – these aren’t converts, they were already Lunar when they got to Tarsh!
In Sartar or New Pavis, conversion rates over the 23 years of Lunar rule were pretty minimal and much lower than people seem to think. 1-3% is probably likely, with at least twice that number being settlers in Wulfland or elsewhere. Again that follows historical norms. The Lightbringers and Yelmalio cults resisted conversion (like Christian resistance in Spain/Egypt or Hindu resistance in India).
So worth remembering that adoption of the Lunar Way by a subject population is always a long-term strategy not a short-term one.