What prevented India/China from being Christianized or Islamicized?

[RINO Tom]

Having entrenched political bodies against such a change that could meaningfully defend their turf for centuries.

I don't think so. India was ruled by the Muslim Mughal Emperors for centuries. And the Chinese dynasties weren't always strong, and their native religions weren't evangelical religions themselves.

The local Hindu leaders managed to have autonomy and due to their numbers and the diversity of religious thought survive these centuries while resisting the central government. Same in China.

Yeah, no ruling power over any part of "India" has ever successfully supplanted Hindu aristocracy.  There is a massive difference between the Spanish completely wiping out indigenous elites in the Americas and the relative freedom of expression awarded to India over the centuries, as far as the effect it has on the long term cultural shifts.

[RINO Tom]

What prevented India/China from being Christianized or Islamicized, unlike most of the world?

 Isn't the premise somewhat flawed in that India is over 1/8 Muslim, With multiple States having a significant Muslim majority? 

Fair point, but it’s worth remembering that Hinduism is effectively descended from Indo European paganism, so the inability to completely replace it is pretty shocking, IMO.  When comparing it to Iberians’ near total Christianization of indigenous South Americans or the Arabs’ near complete Islamification of Persia and the wider MENA region, Hinduism’s ability to live on is quite unique.  I believe it’s the only pre-Axial Age religion to still exist in any significant numbers.