Religion of new born baby

Generally patriarchal are there in Indian society (with some exception in Eastern India) , so the new born baby would be of the same religion as of his / her father professed.

It is your own choice to allot whichever religion you want the child to belong now, once the child becomes adult it can choose its own religion after that. 

Two religions cannot be mentioned in the birth certificate

Mention it as Indian if they dont want any government benefit from government reservation or other benifits.