A few points to consider for missionaries to India in particular, and to overseas missionaries in general:
1. Resist the temptation to make quick judgments. Indian tourists in the US often make this mistake about American society. A recent visiting relative asked me why people walk around in their underwear, referring to the scant summer clothing in the 90 degree heat. The broader view is that American society is immoral. I've heard numerous similar observations which folks make, based on their cultural perspectives. Americans tourists in India are very concerned about arranged marriages, child workers, beggars and so on. Christians are concerned rightly so, but it takes some thought to understand if some of these are actually evils or simply excuses that are used by the unscrupulous to generate evil. More on this later in this post.
2. Attempt to change society only by changing an individual at a time. Do not start a civil rights movement in a foreign country. It is dangerous as well as counterproductive. Focus on individuals who need care or counseling. Do not force your cultural prerogatives on them. You may imagine a bride to be scared witless in an arranged wedding, but it may not be so. The culture takes it as normal. If you were to encourage people to date or men to ask for a woman's hand, it may be perceived as cheap, immoral, intrusive or making unwelcome sexual advances in some cases. I've known women who have sharply rebuked or even slapped men for confessing their affection for them. Many women (clearly not all, as India is a nation in cataclysmic transition) prefer the security of a marriage approved and arranged by parents to one they arrange for themselves.
3. Do not belittle their deeply held assumptions about life. If a worldview needs to change, there must be at least some cultural conflict. That is a given, but so often we assume that Christianity is simply incompatible with some cultures. The Hindu scriptures are a mishmash of different worldviews including panentheism, deism, polytheism and even atheism. If you read a little closely you will see that although their view of the fallen world and the remedies prescribed are not in line with ours, the fears and challenges expressed in them are rightly placed- fears of sin, punishment, honour, duty, righteousness. It is important to affirm that these fears are genuine and that they find their answers in the person of Jesus. Jesus must come into their fears, not what you believe their fears should be.
4. Recognize the evils prepetrated using culture as a cover. Although it is a bad idea to fight traditions such as arranged marriage, you must recognize that some people use this tradition to make money through exorbitant dowries that are used to fatten the parents' wallets or create situations of domestic servitude. Only do not assume that this is the norm- it is not.
5. Pray for sensitivity. Every human being on the face of the earth has some prejudice or other. This is inescapable and it is sinful. The church I'm part of in America has been welcoming and kind; and I feel at home. I have known Indians who haev not felt that way. This will happen when you visit a foreign culture- you may feel unwelcome and you may harbour some form of prejudice against them. Recognize this as fact and ask God to change yourself. After all it is not in living in denial of personal sin but in seeking God's strength to remove sin that we succeed as Christians.