The mixing of cultures isn't just one person assimilating to another culture. They always bring aspects of their culture and those get mixed with the existing culture, that's the great thing about it. We can see it easily in how cuisine varies around the world. american Chinese food is different than Indian Chinese food and American Indian food is a bit different than Indian food in India
But this is part of how society evolves and its not a bad thing, we learn from each other and adapt to new situations. Unfortunately there seem to be those of us who can't adapt and life just leaves them behind. That's how life works. Progress and change doesn't care about personal opinions, it just happens and it has been and always will be a normal part of life