Lots of Asian countries have a common culture that spans groups following different religions: Indonesia, India (and particular Indian regions), Sri Lanka etc.

Also, most of the major religions spread to different cultures a long time ago: A thousand years ago a Russian and a South Indian could have both not only been Christians, but both Eastern Orthodox, or an Indonesian and a Libyan could both be Sunni Muslims, or a Sri Lankan and Laotian could both be Theravadan Buddhists.

If people of disparate cultures could share common beliefs, sure religion and culture have always been separable. Especially pertinent to your examples are the South Indian Christians who have undoubtedly shared the culture of the Hindu majority for 2,000 years.

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.

"Indigenous American and Hindu culture, for example, have traditionally had no such division between religion and culture."

Isn't that just a bias from watching too much discovery channel? We are used to seeing other cultures presented as being preoccupied with fancy rain dances, perhaps because they look good on television. But they must have a "normal day routine", too, which I would consider to be culture as well? It might be the "bag of rice in china phenomenon" - mundane daily life might not make for interesting movies, so we disproportionally often get to see special events from other countries.

I don't think so. I do think there is a problem when we view other cultures from the outside, and when we focus only on the "fancy" aspects of culture because it's more interesting than how people arrange their bedding, or whatever.

However, I think you are focusing too much on religion as ritual specifically. Yes, indigenous Americans, for example, have certain rituals, rites, and special events that stand apart as specific expressions of their unique culture. If those rituals seek to connect the individuals who participate in them, and the community as a whole to an "ultimate reality" or an unseen world, we in the west call it a religious ritual. Most indigenous American people (all, as far as a I know) do not even have a word for "religion," however, so the mundane and the "fancy rain dance" are each simply forms of culture with no defining boundary.