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.