If you take any nation today, regardless of hetero or homogeneity, it will likely scarcely resemble the culture of that nation from 50 years ago, let alone 100. Cultures changing is not really a problem and I think migration is in no way a negative when people assimilate. Assimilation, practically by definition, tends to be a host culture casting away perceived undesirable views and values, while adopting the perceived positive views and values of a migrating culture.
But a failure to assimilate, should the migrant culture become large enough, can result in the exact opposite outcome. Minority views seen as unacceptable may, over time, start to reach the point of becoming politically influential. So for instance, how likely do you think it is that a western liberal nation will criminalize homosexuality over the next 100 years? The question's ostensibly stupid. It's so far outside our trajectory and realm of thought that it seems about as likely as pigs learning to fly.
But just consider one example. Sweden today is one of the most liberal nations in the world with an extremely generous welfare state and an incredibly inviting people. They're also a very small nation of about 10 million people, not long ago it was less than 9 million. And their fertility levels have plummeted. At one point they were literally negative. And their embracing nature has also seen a near open door policy to migration, which is a big part of the reason that their population (and fertility) rates have increased. However, many of the individuals migrating are not assimilating - and hold views which are in extreme contrast to 'Swedish' views. If we assume Sweden continues along its current trajectory, it's not really out of the question to see what is today one of the most liberal nations in the world criminalizing homosexuality and beyond.
That is fundamentally what I meany by a people being exterminated. It's not the 'people' as in a genetic lineage, but the shared views and values that makeup a people. There will certainly be people that call themselves Swedes in the future. But the views and values of this nation may end up regressing (from our perspective) dramatically in the future. Centuries of progress and social development cast aside in what could be a matter of decades for a lack of fertility and a refusal to consider the implications of nonassimilating migration.