It's pretty good, but our calendar and celebrations and acts of remembrance/memorialisation are all steeped in it - or at the very least derive from religious practice. When I think of pure representation of a culture, elements that distinguish one from the other, I immediately think of those more notable occasions (particularly the way we memorialise the dead).
How would you define your culture? And how would you consider it to be ruined or supplanted by immigration? Eg. what's your worst case scenario 'We no longer have/do X therefore my culture is dead'?
No culture ever dies completely, unless it's all out genocide, which really wasn't that unusual even a few hundred years ago, and arguably still happens on a much smaller scale in certain parts of the world.
In any case, objectively there are but very few cultural traits I would consider incompatible and a bad addition to a hypothetical melting pot result. It's not so much about the culture being "ruined" and "supplanted" as the fact that, devoid of any judgements about "good" or "bad", a bunch of european cultures were and still are to a certain extent unique. I don't think, say, Saudi Arabia should import tens of thousands of irishmen. I'm sure their culture would be enriched by such a vibrant exotic addon, but the area, like every single other fucking area on the planet, has a unique cultural legacy inextricably attached to the people and the land. And in any case they have absolutely no interest in such a thing. They are proud inheritors of a cultural tradition, heavily rooted in religion, that has shaped a gigantic area over more than a thousand years. They have no interest in abandoning that for some cultural engineering experiment. No other cultures on the planet do. The chinese harken to a legacy stretching back thousands of years. The entire indian subcontinent are fiercely attached to their myriad denominations, cultures, ethnicities. The examples are as endless as there are tribal identities that people adhere to. Despite similar situations in europe, all of this past, this idea of being a link in a great chain, of, yes, respect for your ancestors and their accomplishments and what they built (as biased and propagandized and mythologized as it always is regardless of culture), is being pretty much abandoned.
I guess that's when I think the cultural shift will have become so wide that it won't recognizeably be the same culture anymore. It's already pretty much here, as Tibe shows.