What are they replacing anyway?

Genetics? The US is literally a nation born out of immigration and any "racial distinctiveness" in Europe has more to do with the limited means of transport leading to geographical inbreeding than some metaphysical legacy of pure bloodlines. Not to mention that most of Europe experienced various migration waves all the way back to the first migrations that resulted in Europe being settled by humans at all. Japan has been trying to keep up its strategy of just being extremely racist post-WW2 and it doesn't look like that got them anywhere.

Culture? You literally can't look at most nations' cultures without also considering the cultures of their neighbors that influenced them. As much as ethnonationalists like to pretend otherwise, for any continental culture the grouping of what aspects are specific to that "nation" have more to do with its history of government than any shared identity. Germany for example was barely a coherent concept before the 19th century. Japan being forced to spend most of its history navelgazing and sitting on its thumbs because it consisted of a bunch of islands doesn't make its culture any more special or worth preserving than any other and most of what you imagine when you think of Japan today is the result of being repeatedly carpet bombed and literally nuked after trying to do an imperialism to the point of voluntarily acting as a vassal to its victor: Westernization had less to do with immigration and more with global trade and trying to cargo cult the nation that wiped the proverbial floor with it.

Heck, the only example I can think of literal replacement is far-right Israeli settlers moving into houses of Palestinian families after their expulsion without even giving them enough time to clear out the fridge. That's literally replacement: residents of one culture and ethnicity are forcibly removed from their own homes and replaced with residents of another. But again, that's not what's happening with immigration and it's not what you're complaining about.

If you're truly concerned with a loss of culture and every distinctiveness being washed over until all that remains is a homogeneous grey soup Disney can fill in a tin and sell to you, the problem isn't immigration but commodification and tourism. Instead of dishonestly grandstanding about native Americans you should be looking at Hawai'i where Americans bluntly annexed the kingdom, cut up the land to sell it off to American hoteliers and the very rich, and then sold off cheap immitations of the native culture so middle-class tourists could have an "exotic" experience as a piece of escapism.

Forget about "national identities". Places used to have identities. Every city, every town used to have a distinguishing character that was the result of its geography and history, like the rings of a tree telling the story of past seasons. Then big box chains stomped out the local businesses and undercut the competition by making it up in volume before ramping up prices again once noone else was left. And with nobody left to perpetuate the culture now that the only means of production was commerce and commerce was owned by the same big companies, all that is left is the same, market researched, focus group tested, mass produced, grey soup that is served everywhere. At best you can hope your local history is interesting enough that Disney picks it up as a novelty so it can use it as the backdrop for its umpteenth retelling of a story some dead guy wrote before copyright became a thing.

You don't seem to genuinely worry about losing culture. It sounds more like you just don't like "foreigners" to live around you. If you are truly concerned about loss of culture, look at preservationist projects. There are for example linguists who go out to communities in Europe who speak endangered languages so they can be recorded and studied. There are people who form activist groups to get local sites on the list of UNESCO World Heritage sites so it becomes easier to find funding to maintain them. There are groups who learn and teach endangered arts or crafts so the knowledge isn't lost when a profession is no longer deemed economically useful. There are people who use spare rooms to run donation-funded private museums to preserve local history.

But here's the thing: culture changes and evolves over time, especially at the intersection. Life isn't static and neither is history. If you demand that immigrants "assimilate" you are literally asking them to give up their culture to preserve some kind of shrinkwrapped carbon copy of what you think yours is. But even if left to its own devices, your culture would change over time. What happens with immigration is not replacement of culture but a merger. Culture is a river, not a pond. No matter how much commodification tries to tell you otherwise by trying to sell it to you in a bucket.