What you say is true, as far as I know. It is entirely possible to share the culture of the people who one lives nearby and yet practice a different religion. It is also true that this has been going on for a long time. In the case of the spread of Abrahamic offshoots (Islam and Christianity), a couple of thousand years. In this sense religious expression has always been fluid. However, I think that is different than viewing religion as an object. It is a modern move to split culture into many different categories: public, private, family, government, religion, education, medical, etc, etc. This way of understanding and ordering the world is a particularly Western (some might say Germanic) form.

Furthermore, there are languages that still survive to this day that have no word for "religion" as such, something I talk elsewhere in this thread. This says to me that in some cultures religion cannot even be conceived of as separate from culture because the language does not provide the imaginative capacity to understand it that way.

So, always fluid, yes. Separable, I don't know.