What prevented India/China from being Christianized or Islamicized?

[The Right Honourable Martin Brian Mulroney PC CC GOQ]

I'll answer for India (based on an admittedly foreign understanding) because that's the one I know more about:

1. India is huge. If you combine the populations of the entire Arab League, Iran, and Turkey (essentially the places that saw the most thorough Islamicization), you're still at less than half of India's. Granted these are based on modern figures, but it would have been impossible to assimilate Indians in any way. In fact, not even Indian-origin empires like the Mauryas and Guptas were able to assert any homogeneity in India.

2. India did get Islamicized, in part. Pakistan and Bangladesh are results of this, and India itself has 195 million Muslims today. And the influence of Islamic rule affected Hinduism and Hindu societies too - but they have largely maintained their character.

3. Most of India never had a wholesale, top-down imposition of Muslim rule the way other ancient, non-Islamic civilizations like Persia had. The only Muslim empire that was able to seriously assert its authority over most of India were the Mughals, who were known for running a very decentralized government that delegated many powers to local rulers, most of whom were Hindu.

4. The Mughals also didn't crack down on the preservation of Hindu traditions and literature in any serious way. There were limited instances of destroying temples and idolatry, but on the whole, the preservation of Hinduism was ensured by local rulers and Brahmin (high-caste) scholars.

5. The Mughals themselves (partly) assimilated into India. The Urdu language emerged from this - originally the Mughals spoke Persian, but eventually switched to Urdu, which is an Persianized version of the Hindi dialect spoken in Delhi (the Sanskrit-heavy version of this went on to become standard Hindi). This is only one example, but imposing Persian and Islamic norms was not tenable in a massive society which already had an ancient and deeply held tradition.

The British did even less to Christianize India. They did encourage missionaries, and the impact of this is most visible in South India and Sri Lanka. But for the most part, like the Mughals, they delegated a lot of power to local warlords and Brahmins.

[The Right Honourable Martin Brian Mulroney PC CC GOQ]

Slightly off-topic, but interesting nonetheless: many scholars have argued that caste emerged as an institution of Hindu society under Muslim and Christian rule. The British did not create the caste system, this is a common misconception. Caste is as old as India. But before Muslim and especially British rule, the system was a lot less rigid, and far from homogenized. But in the absence of effective local government, and under the rule of an aloof and ultimately foreign ruling class, high-caste Hindus emphasized traditions like caste as a means of preserving social order. The British Raj was happy to systematize and enforce this by law, because they were smart rulers - they knew that maintaining order in their empire by manipulating indigenous concepts would be more effective than sending redcoats to every little village and enforcing their laws at gunpoint.