At the height of the Mughal Empire, it encompassed most of what would later be considered India, with the exception of the far south. You can argue that an empire is not a country, but if we argue in that way, well for most of European history, Europe didn't have countries either.

> Even Bengalis, a distinctive ethnolinguistic group, are divided between India and Bangladesh based on religion, which is a major division—a much bigger one than the religious divisions that differentiate countries in Europe.

There is a significant minority of Bengali Muslims in India, and a smaller minority of Bengali Hindus in Bangladesh. The Indian-Pakistan and India-Bangladesh divides have never neatly followed the religious divide, certainly never as neatly as religious nationalists on both sides would have it.

> For example, France and Spain—both are Catholic, and their languages were considered merely different dialects of Vulgar Latin until the 1400s.

Old French and Old Spanish were already identifiably distinct languages by the 9th century. Some argue (following Robert Wright) that a major impetus for them becoming identified as distinct languages was Charlemagne's Latin pronunciation reform. Prior to Charlemagne, Latin in Romance Europe was pronounced based on the local dialect – so the same Latin text would be read aloud using a French pronunciation in France, a Spanish pronunciation in Spain, an Italian pronunciation in Italy, etc. Monks from Britain and Ireland, having no indigenous tradition of Latin pronunciation, instead devised their own based on phonetic spelling. Charlemagne's advisors convinced him (however incorrectly) that the British/Irish tradition of pronouncing Latin was truer to the original, and so he imposed it on the Church–which suddenly made Latin and the vernacular seem like much more different languages. Now, that said, Wright's thesis is controversial – but even its academic critics, I don't think many of them would agree with you in putting the distinction between vulgar Latin and Old Romance so late.

And, while no denying the difference between Islam and Hinduism is bigger than difference between Catholicism and Protestantism, Europe shows parallel cases of countries with a common language and culture, where the major difference is the dominant religion – the primary difference between Austria and Germany, is the former has traditionally had a Catholic supermajority with a small Protestant minority, the latter was traditionally dominated by Protestants, albeit with a large Catholic minority.