You have raised a very pertinent question. Although, in our patriarchal society, the answer to this is very clear. If someone is Christian or Muslim or Hindu or no matter what , the child of that person will be by default included in that religion, if the person is a male. If we are talking about a female who is either Christian or Muslim or Hindu, then her child will be the bearer of her religion, only if, she is married to some male member of the society sharing the same religious identity as of her.
If you raise the question that whether caste or religion is important in a child's application form, then the answer is yes. It is important for school/ college admission, admission to vocational schools, application forms for voter identification cards, ration cards or even passports. So as you can see that there is no legal document where you can skip the religion part. The answer to the question, whether this caste identity is important for the child to grow up as a good and rational human being and a society contributor is a big 'NO'.
But the tragedy is that although our society has become modern and today we have 'others' category in the gender section, we could not eradicate the caste option in the application forms.
But the good thing is that the private sectors are great pioneers in this regard. In private sectors mostly the application forms include only those information that are necessary to get the job. Neither they have reserved quota for any section of the society, nor are they interested in what religion you belong to. So you can be of any caste, but you will have to secure a job by virtue of your talent not your caste or religious identity.
Live life Kingsize!