Can Christ be your saviour, without being your religion?

On more occasions then I care to recall I have heard or read people saying that Christ is their savior,  but not their religion or that Christianity is a relationship and not a religion.  This always confuses me.

According to the Merriam-Webster dictionary Religion is

a : the state of a religious <a nun in her 20th year of religion> b (1) : the service and worship of God or the supernatural (2) : commitment or devotion to religious faith or observance
: a personal set or institutionalized system of religious attitudes, beliefs, and practices
archaic : scrupulous conformity : conscientiousness
:a cause, principle, or system of beliefs held to with ardor and faith
Do the people who say Christianity isn’t a religion not commit themselves to God? Do they not have a belief system? Do they not have faith in God?  While if you are a Christian; Jesus is your savior,  and you are supposed to have a relationship with him, I really need someone to explain to me how they can be a Christian without having a commitment, faith, or even a system of beliefs that center around Christ. If they have those things Christianity is their religion!

James 1:27
Religion that God our Father accepts as pure and faultless is this: to look after orphans and widows in their distress and to keep oneself from being polluted by the world.