Asklemmy

It's because Christianity incorporated a lot of pagan rituals into Christianity and some pagan gods became catholic saints.

The crusades targeted all religions that weren't nicene christian and they were especially cruel if you were christian but not nicene.

Lookup the history behind the Dominican order if you want more gory details

Besides the other reasons mentioned here, i think there is a strong factor in the social and intellectual sphere. Christianity was a cohesive standardized institution with a written holy book (or set of texts, before the council where they canonized which books would go to the bible), and later became a part of enforced state policy. That mixture of standardization and officialdom allowed it to essentially accumulate 'capital' to such a degree it could (after absorbing lots of ideas and practices) overwhelm the local polytheistic societies and religions.

Local polytheistic religions were extremely varied, and each village tribe or city had its own gods, beliefs, etc. The mess of beliefs meant that the religions spread organically, not in an institution with quasi industrial ways (standardized beliefs, practices, texts, even rows of clergy trained in the same ways on churches and monasteries). They could be challenged and be overwhelmed by the bigger faith, in intellectual ways (evangelization) or by demographic superiority. Or just by immigration to other regions (which many people did, like the barbarians in late Rome or Imperial legions and soldiers since always), where multiple contradictory faiths coexisted, until a cohesive unified alternative popularized.

All that is inverted in India. Hinduism was (is) varied, but way less than paganism from ireland to iran, and it is a formalized institution with written holy texts supported by the state (or by castes, specially the Brahmins), very constant and stable over many generations. That inertia even allowed it to not become muslim majority (except in a few regions).

Other countries in Asia actually have Buddhism as the main religion or state religion (or main historical religion). Even if buddhism absorbs lots of pagan deities, ideas and praxis, the core institution is solid and formalized, and dominant. Japanese Shinto is very different from pre buddhist times. China had buddhism, and confucianism and taoism as also very standardized formalized state institutions (aka not a different religion per village). So asian polytheism is very reduced compared to european one.

One factor is that paganism is tolerant of adding additional gods, practices, or beliefs to your mix. From a pagan standpoint, adding in Christianity wasn't a big deal, but Christianity was not similarly tolerant, they weren't cool with you keeping your pagan gods. Plus their belief system had the threat of eternal damnation and the promise of heaven to motivate you.

Christianity

Within the Roman Empire, Christianity ended up succeeding as the apocalypse cult within the empire, with Rome eventually foresaking the old gods for Jesus.

As Roman retreated, Rome's church survived and became a unifying force in Europe. While there were crusades, there were also cases of willing conversion in order for border nations to gain access to the European market and diplomacy.