Yes, I was wondering if Iran could go Bahai.
Your POD is really interesting.Like you mentioned in the OP, a number of Albanian intellectuals toyed with the idea of a mass conversion in order to solicit further western support. Catholicism is not a viable option due to previous tensions and antagonism between Muslim and Catholic tribes in the North. Historically, Protestantism attracted the most attention and I think with an early enough POD you might be able to get something going...here's one idea.
A Mughal converting from Islam to Hinduism could mean a mass conversion of northern Indian Muslims, possibly allowing India and Pakistan to remain a separate entity after colonization, provided butterflies are't too crazy.
Considering Islam was part of the core of the Mughal identity I really don't see that happening.
I actually think that you could get a good sized conversion on similar principals. You just need some scandal or misplaced political support by a major Islamic leader that looks really bad for Islam without affecting other religious groups. Religions often suffer when picking the losing side in a civil conflict. Have that happen in a heavily Islamic country that is democratizing and has sizeable minorities of another religion and you could see those minorities explode, especially if they have a palatable connection to the nation's past that the nationalists are attracted to.Now, in the case of a population in which Islam is the long established religion I really don't see it happening en masse, I mean individual and even small scale mass conversions (as in a single village) are possible and have happened, but unless being forced for generations, I really don't see it ever happening; the Abrahamic religions are very good at retaining believers and Islam is even better at that than the others; the only real 'threat'/likely population shift is to simply no longer believe in religion at all and becoming Irreligious (Atheist or Agnostic), however by that point the population is'nt going to see any other religion as the true path since they'll view religion in general critically.
I actually think that you could get a good sized conversion on similar principals. You just need some scandal or misplaced political support by a major Islamic leader that looks really bad for Islam without affecting other religious groups. Religions often suffer when picking the losing side in a civil conflict. Have that happen in a heavily Islamic country that is democratizing and has sizeable minorities of another religion and you could see those minorities explode, especially if they have a palatable connection to the nation's past that the nationalists are attracted to.
So, just to use the first idea that comes into my head, post Ottoman Egypt (in a scenario without British control of Egypt) might work. They have a democratic revolution in which Muslim authorities support the Muhammad Ali Dynasty, and the Coptic Christian leaders support the revolution. Eventually Coptic Christianity becomes associated with the revolution and their idealized nationalistic vision of Egypt, while Islam is considered to be imposed by foreigners and not culturally Egyptian. The revolution succeeds, but doesn't force people to convert. Early democratic rule is very successful, and inspires large numbers of conversions. Similar revivals of pre-Islamic religions might possibly take place in other countries provided they have a large enough minority religion to still be considered relevant.
Not incredibly likely I'll grant, but neither is any possible peaceful mass conversion.
France had the same relationship with Catholicism, but the church kept picking the wrong side in civil conflicts. France didn't have a viable religious minority to turn to, so irreligion was the result, but Egypt does, so assuming the Copts pick correctly I could see a national myth that portrays them favorably arising and garnering some converts.Egypt is not a very good example here since it's long considered itself to be a Center of the Islamic World and takes great national pride in it.
France had the same relationship with Catholicism, but the church kept picking the wrong side in civil conflicts. France didn't have a viable religious minority to turn to, so irreligion was the result, but Egypt does, so assuming the Copts pick correctly I could see a national myth that portrays them favorably arising and garnering some converts.