As I understand, Culture is what people do in common, like in common and pass it down to their offsprings (Hindu Culture, Indian Culture, Western Culture). I agree with Aditya Mohan, who we are now is a reflection of our culture. Religion is each one's way of accepting that there is a higher power above us and there are many paths to this faith ( Hindu, Muslim, Christian etc).
Over a period of time culture undergoes change but it's difficult to give up our culture. For instance, Indians living in the West seek out or build places of worship of their faith. Many Indians living in USA or UK, enroll their kids in Sanskrit, Bharatanatyam classes and perform head tonsuring or naming ceremonies as per the Hindu culture and tradition. This reflects their desire to follow, pass on and preserve their cultural origins. The same may be true for people of other religions in India.
Sometimes culture is given a darker shade when people misuse it for political and personal gains. Following a particular religion for the welfare of oneself and people around is accepted, so also should people who believe that the world is one be accepted.
Change is inevitable and the world is caught in it. Whatever our cultural background is, we should move forward carrying along with us the good things what our culture has taught us because it has the wisdom of many generations over thousands of years that the urban society cannot give us.