Well the issue is one Indian Christians struggle against and some of the prejudices are deeply ingrained, I don't know if foreigners can easily understand the context, but I will try say something and be objective as well.
Hinduism has a way of assimilating external influences to itself; when Buddhism was a strong force in India, Orthodox Hindus fought long and hard polemical wars against it; but today most Hindus would claim that Buddhism is just another member of the large Hindu family sharing many of same dieties especially with Tibetan Vajrayana Buddhism, Buddha being made into a avatar of Vishnu etc etc.
Outside every church and shrine, especially those dedicated to the Theotokos, there is usually long line of Hindus lighting candles, decorating the icon with flower garlands etc; many will acknowledge the divinity of Christ, but will not make a formal conversion. Many will keep an image of Christ with the images of their dieties and thus co-opt Christ into the Hindu pantheon. Such an assimilating trend has meant that people and religions have been allowed to enter India, with little persecution (unless the Hindu socio-economic system is gravely disturbed)
Hinduism and the customs that flow from it have greatly influenced every religion that made it to these shores. Christianity has not been an exception.
A very rigid caste system existed in Kerala till the 19th century, as can be understood it was natural that some abuses would creep in from such a culture.
The Syrians Christians of Kerala believed themselves to be converts to Christianity from the higher Brahmin caste ( it is believed St Thomas converted seven Brahmin's who were having a ritual wash in the pond). The next major wave of conversions to Christianity only occurred when the Europeans started arriving in India in the 16th century.
During this long time gap, the relatively small group of earlier converts were almost accommodated by the higher Hindu castes , accorded similar social status, allowed to build churches , rule themselves and generally prosper; in return I believe Christians were encouraged not to aggressively seek conversions and disturb the Hindu social order. I believe small groups did convert and come over at one time or the other, but no large scale missionary attempt by Indians seems to have taken place.
I think the Syrian Christians in India paid that price which was demanded of them during that period (it should also be understood that the Christians in India were dependant on bishops from East Syria and there were long absences without bishops, in such cases the community was weak and under pressure ). The king, the ruling and priestly classes were all Hindu, so some sort of accommodation was also a matter of survival. The community seems to have turned inside ( like the Jews of the diaspora did) , rejecting most external influences in the context of faith. This is one reason, why we survived as Trinitarian Christians through those long centuries with very little contact with the rest of the Christian world, without descending into syncretism (that temptation is always strong, even now)
When the Europeans and especially the Jesuits and English CMS arrived, relations with the Syrians were often sour because of our allegiance to prelates in the Middle East, so they aggressively sought conversion from the economically and socially deprived lower castes. As can be imagined mass conversions from such communities did take place.
Such RC converts became members of the Latin Rite( so the eastern rite Syrian catholics did not have a problem as they had their own parishes), among Anglicans however when parishes had to be shared between the Syrians and the new converts, problems occurred. The "syrians" were not happy, the new converts were uncomfortable and so on. In many a case separate parishes had to be erected in the same village for the two groups. The Orthodox did not have a large scale mission to other communities at that time, so we like the Catholics did not have a problem.
Later beginning in the 1880's, St Gregorios of Parumala and Mar Osthatheos Petros worked among the lower castes converting many to Orthodoxy ( strictly understanding it to be a temporary measure , separate mission parishes were raised for them ). I believe 50-60 or more such parishes exist even now.
However this is not to say that prejudices did not exist till very late. Marriages are arranged in Kerala mostly, so families search for a spouse from families of a similar status, that has meant that no intermarriage takes place between the syrians and non-syrians.
This "syrian" identity as converts made by the Apostle is taken a bit too seriously and even Pentecostals ensure frequently that intermarriage takes place. Frankly marrying from the non-syrian communities would be frequently seen as marrying below ones station. All this has meant that dalit Christians frequently feel marginalized .
Also a lot of Dalit Christians were recruited to work as farm hands and household help in Christian households( higher caste Hindus would not do so, this meant that a large number of dalit Christians were employed in Christian homes), this also meant that one could socialize to a limited extent with those in your employ. So prejudices exist, Kerala has led the country in trying to erase the old caste systems, this has meant that positive changes have been seen amongst the Christians as well.
The churches in India have not reconciled themselves to casteism officially; but yes there are many, including the clergy who would like to sweep this thing under the carpet and be happy with the status quo. Everybody knows that as Christians we are all equal in theory, but putting it into practice is difficult.
This difficulty is a shame, and it is this shame that allows many to be silent and pretend the issue does not exist.
Regarding mission and evangelization.
Most western Christians even Orthodox do not see Hinduism as more than idol worship, demonic is a word often used. While Hinduism definitely has many troubling aspects, this characterization as demonic often leaves many Indian Christians including myself dissatisfied. A lot of mission work that has been guided by American protestant techniques has taken place which does not seem to see even one good thing in Hindu culture. Such converts are often left theologically and spiritually as strangers in their own land. So instead of perceiving Christianity to be old and natural to India, it is seen as something alien and western.
Also aggressive conversions that involve idol breaking, picture smashing etc has led to a reaction from the Hindu Right and violence against all Christians has now become more common.
The Orthodox traditionally did not pursue protestant mission tactics; we built schools , hospitals , orphanages etc but "winning souls" has not been a overriding priority. Most priests are happy to have Hindus attend worship regularly, learn and discern and conversions are done after substantial periods of time. A Hindu girl who does not know Malayalam converted to Orthodoxy in my parish recently. So conversions do take place, but western style mission is not pursued. The general feeling is that such missions have done more harm than good. Similar trends are seen also amongst Eastern Catholics and in the Latin Rite.
Each nation has to learn to reach out with the Gospel in its own way, and in India that seems to be finally starting.