I think that Buddhism, particularly Vajrayana Buddhism would fill the niche that Islam filled in India in the early modern period. Or quite possibly Catholicism.
For India not to be subject to Muslim invasions, the Hepthalites would have needed to remain strong in Afghanistan and not succumb to Sunni Islam themselves, but remain Buddhist and fend off the armies of the Caliphate. We might then see repeated Buddhist invasions from the north, both from Afghanistan and from an unexpected direction, the Tibetan Empire during times when Tibet is strong and North India weak (the 800s-900s). Those invasions would bring Vajrayana Buddhism which would become popular amongst the untouchable castes.
Because it was the untouchable castes, the Dalits who IOTL were, not surprisingly, most attracted to Islam when the Muslims conquered parts of India. They had nothing to lose by identifying with the conquerors and rejecting the outcast roles Hindu society thrust upon them. And from the 1920s on, when conversion to Islam or Christianity became less attractive for Dalits because of Indian nationalism, the Untouchable Liberation leader Ayumbdekar (I hope I have the spelling right) led untouchables to convert to Buddhism--usually Vajrayana Buddhism in mass conversions( which are quite offensive to Vishva Hindi Parishad and their militant arm Bhajrang Dal activists) today IOTL.
And from the 16th Century on, I can see first Catholicism brought by the Portuguese and later Protestantism brought by the English gaining much more of a following in India than they have IOTL. All without affecting Hinduvta's position as the dominant religion.
One important butterfly: Without a Muslim presence in India, the British are not going to be attracted to Sunni Islam as a foil to HInduism the way they were IOTL. This will directly affect how the UK approaches the Middle East ITTL. IOTL, the British supported Sunni Islam, Deobandi Sunni Islam, after the Sepoy Rebellion because they feared Hinduism and Hindu nationalism. And since colonies and protectorates East of Suez such as Aden, Oman, the Trucial Coast (now the United Arab Emirates), Bahrain, and by the turn of the 20th Century, Kuwait were governed out of India, knowledge of, comfort with and a bias in favour of Sunni as opposed to Shia Islam became well established in the Indian Colonial Office. Which is where the relationship between the UK and the House of Saud initially developed and was cultivated--to the point where the Saudis could be supported in a conflicting claim to first the oil rich Persian Gulf Qatif and then over the rest of the Arabian Peninsula, particularly the Holy Cities of Mecca and Medina, over and above the Hashemites who ruled the Hejaz and revolted with British support (and the help of T.E. Lawrence) during WWI against the Ottomans. To the point where the British stood aside and let the Saudis blatantly violate international law and conquer the Hejaz and Asir in 1921, long after Middle East borders were established by the Treaty of San Remo and belatedly setting the Hashemites on thrones in Transjordan and Iraq as compensation for their double-cross.
None of this is likely to happen ITTL if the Muslims are not in India. When the British approach the Middle East, they are likely to look very differently at Persia (soon to be Iran) and Shia Islam if they are not approaching both with vested interests in favour of Sunni Islam already established in India. They may find Persia, which contains both Russia and the Ottomans much more important and work directly with it as an ally instead of continually trying to hobble it as the UK did IOTL.