If we're assuming that the Caliphs fought off the Mongols in 1258 and Baghdad wasn't sacked, it's hard to see where a Timurid Empire would come from. A Zoroastrian Persia? Hmm, this might be justified historically... in 755 Abu Muslim's execution provoked rebellion against the newly installed Abbassid Caliphs. One rebellion was led by a Zoroastrian, Sunpadh who preached a kind of Muslim - Zoroastrian syncretism. 755 was also the year of the battle of the Talas River. But suppose the Chinese had won and advanced into Eastern Persia? The rebels, backed by China, might have triumphed, and a modified Zoroastrianism could have become re-established.
The Caliphate loses Persia permanently at this point - so when the Mongols arrive, are they too weak to defeat them? Or maybe it was this new Persia that defeated the Mongols... then we keep them out of the Muslim world altogether! In Central Asia, almost any religion could have won out - the Turkic peoples were variously Nestorian Christian, Manichean or Buddhist before Islam advanced.