Christianity will likely spread to all the regions it did IOTL by 1500, plus the Sahel. Persia is a big question mark, but I'm of the opinion that Zoroastrianism (which by this point was an ethnic religion, the faith of Aryan peoples par excellence) is unlikely to die out on its own without a foreign conquest. Absent a Christian conquest of Iran, Central Asia and the western steppe would likely remain a religious hodgepodge, with some Christian rulers but no Abrahamic religion ever becoming dominant.
India will not convert. Southeast Asia I'm less sure about, since the OTL conversion of the Archipelago to Islam was strongly influenced by India's conquest by Perso-Turkic Muslims. China will not convert.
There's this meme going around in this parts that China inevitably Christianizes without Islam. No evidence is ever provided for this.
Muslims and Christians did not compete in China. Nestorian Christianity largely died out in the late Tang because a) Emperor Wuzong stamped down on foreign religions trying to convert people and b) unlike Manichaeism, which survived into the Ming in increasingly Buddhism-adulterated forms, Chinese Nestorianism was apparently not very open to Chinese converts rising high up in the hierarchy. Islam survived the Tang, and every following dynasty, because Muslims did not attempt to proselytize to Han Chinese. The modern Chinese-speaking Muslims (the Hui) are descendants of Muslims who immigrated to China and assimilated into Chinese culture.
The non-proselytizing Muslims did not compete with Christians for converts, and the presence of Muslims was completely irrelevant to the death of Christianity in imperial China. In a world without Islam, there might be a small Christian minority akin to the Hui, along with some Christian-influenced cults (like the Manichaean ones OTL) whose followers inevitably abandon the religion when they miraculously manage to gain power (just as Zhu Yuanzhang banned Manichaeism OTL). There is absolutely no reason China converts to Christianity.
Zoroastrianism was basically like a bigger Judaism by the point Islam came around. Sasanian orthodoxy did not really accept the notion that the faith should be spread to non-Aryan peoples.
The Uyghurs might beg to differ.