It is known that many Indian Christian women wear head coverings during religious services. They may cover their heads with the end of a sari, which is a traditional garment worn by Hindu Indian women.
This is in fact a Christian tradition coming from Paul:
I commend you because you remember me in everything and maintain the traditions just as I handed them on to you. But I want you to understand that Christ is the head of every man, and the husband is the head of his wife, and God is the head of Christ. Any man who prays or prophesies with something on his head disgraces his head, but any woman who prays or prophesies with her head unveiled disgraces her head—it is one and the same thing as having her head shaved. For if a woman will not veil herself, then she should cut off her hair; but if it is disgraceful for a woman to have her hair cut off or to be shaved, she should wear a veil. For a man ought not to have his head veiled, since he is the image and reflection of God; but woman is the reflection of man. Indeed, man was not made from woman, but woman from man. Neither was man created for the sake of woman, but woman for the sake of man. For this reason a woman ought to have a symbol of authority on her head, because of the angels. Nevertheless, in the Lord woman is not independent of man or man independent of woman. For just as woman came from man, so man comes through woman; but all things come from God. Judge for yourselves: is it proper for a woman to pray to God with her head unveiled? Does not nature itself teach you that if a man wears long hair, it is degrading to him, but if a woman has long hair, it is her glory? For her hair is given to her for a covering. But if anyone is disposed to be contentious— we have no such custom, nor do the churches of God. (1 Corinthians 11:2-16)
For an exposition of what the last verse means: 1 Corinthians 11:16.
So the question is rather why Western women do not go to Church with their heads covered: Uncovering the Head Covering Debate.
In cultures where headcovering is the norm anyway, there is less push to abolish the custom and thus women still wear the head covering. It was also in fact a Christian custom.
I think you are confusing two different things. All most all Indian Christian women use the end of their sari as a veil during a christian religions service. This is purely for convenience, nothing else. They cover their head for the same reason why Christian women all over the world cover their head. Also not all of them cover their head outside the Church.
That said in some Indian cultures sari has to be worn covering their head. It has nothing to do with religion. That's how it is worn. It has become a cultural thing. I don't think '
why' can be explained.
So those women who cover their head do not necessarily mean they are christian or do their attire represent their faith in any way.
P.S: Also one cannot be culturally Hindu and Christian by faith. May be you meant culturally Indian.