What prevented India/China from being Christianized or Islamicized?

[Statilius the Epicurean]

Muslim states dominated the subcontinent from what, ~1200 to ~1750? Over the same length of time of about 600 years from conquest Egypt had only very recently lost its Christian majority and there were still large religious minorities in the Levant and Iran. Really though Hindustan was a very large and decentralised country and Muslim rulers generally cut deals for support with local Hindu elites like the Rajputs or Brahmin administrators. And it's reasonable to venture that they were reluctant to convert to Islam because their social status was mediated through caste: going from proud Brahmin to ordinary Muslim (who would still be ethnically below and separated from the Turco-Persian Islamic elite) was not a very attractive proposition.

As for China, social advancement was through the imperial examination system based on memorising the Confucian classics. So converting to Islam or Christianity would get you nowhere. Matteo Ricci tried to convert mandarins at the court and only had limited success by introducing them to Euclid and western astronomy.

[Statilius the Epicurean]

*As an aside, why did Christianity hang on for much less long in the Maghreb?

I think Christianity had less of a hold on the Berber population of North Africa, who were always kept at arms length by Roman rule.