Do you have sources to back that up? I'm genuinely curious. My understanding was that marriage was always a social contract, but that society and religion used to be more intertwined thus 'religious marriage'.

I don't disagree with the idea of separating the religious and civil/cultural aspects of marriage. But I think you'll find non religious folk resistant to calling civil/cultural partnerships something other than marriage. It's a deeply embedded cultural concept not just a religious concept.