"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.
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.