An exaggerated example, but a good litmus test here is something simple like are you ok with lots of Americans moving to country X (let's use China and Norway) and making it culturally more like America? You can't say that this is a problem but then Iceland (since that's the example we're using) being weary of accepting large numbers of immigrants out of fear of culture change isn't a valid concern also.
The country has also signed up to accept practically unlimited immigration. It's a part of the EEA (the economic area of the EU), meaning that a population of around 500 million can move there tomorrow with very few legal hurdles. "Unlimited" in the sense that the difference between 500 million and the world population of 8 billion hardly matters for a country with a population of far less than 1/2 million.
1. https://www.hagstofa.is/utgafur/frettasafn/mannfjoldi/mannfj...
2. https://www.census.gov/content/dam/Census/library/publicatio...
All things being equal, how many people want to flock to Iceland to work in tourism and fishing? Maybe with the right immigrants one could replicate their last financial bubble & crisis.
I don't know about Norway or Iceland specifically, but I have been told that English is so trendy in Sweden that not a lot of cultural works are actually written in Swedish anymore. As for China, we've actually gotten cultural backwash from Hollywood doing so much business there. Specifically, a lot of western media companies have had to self-censor in order to retain Chinese market access.
If we really wanted to coat every culture in amber then we would need a lot more than just immigration controls. We would need to emulate pre-Meiji Japan in every country in the world: i.e. no migration whatsoever, and heavy restriction and censorship of cultural imports. So no Internet, no imported cinema or TV shows, no international phone calls... hell, no international postal system.
Less dramatically you have countries like Canada or France that have local content quotas, but those have their own issues. But those are less "stop cultural change" and more "keep Hollywood from completely smothering our local creative industry".
> If we really wanted to coat every culture in amber then we would need a lot more than just immigration controls.
Following this extreme reasoning we should equally just dissolve all borders. Let's start with Japan or Switzerland perhaps? I've always thought it would be cool to live in Switzerland myself. I'm disappointed I can't retire to the Scottish countryside or to Brittany. Who are they to tell me I can't live there?
Obviously this is a non-starter, but being dismissive of others wanting to hold on to their contemporary culture is ridiculous too.
indeed, the dodo would agree