I think there's a key concept missing from every discussion about culture, and that concept is that "X immigrant culture" is a completely different culture from "X culture." Indians in India have one culture, while Indians in e.g. Britain have a related, but divergent culture.
Two places this matters:
• Frequently, the people of "X immigrant culture" care a lot about 'preserving their heritage', because it's a constant struggle for them—while the people of "X culture" couldn't give a damn, because they're constantly steeped in their own culture and it's not going away. "Cultural appropriation" is an invention almost entirely of immigrant cultures.
• People "exploring a culture" frequently have the implicit goal of exploring the domestic-immigrant offshoot of a culture, not the native one. Because of the lack of connection and cultural touchstone organizations that immigrants face, things like dances and dishes are seen as far more relevant in immigrant cultures, similar to their role in itinerant cultures.