Ui, this is an interesting one, as I strongly disagree on a few parts.
First - language is upmost important to understand a culture. It is an expression of the culture itself, there's a good reason that many words are not translatable and are taken into other languages just as they are - because the other culture has no feeling for this specific experience described. Yes, you can learn many things about a culture observing, but you can only be part of the culture, really experimenting it, learning the language. The language is the first step (saying a few words on the market buying veggies), and it is the path into deeper understanding (if wished so).
And yes, as a foreigner, we have to learn history, music, poetry and such in order to understand the culture, to get a better hold of it. The natives don't have to. They grew up within the culture, it's intrinsic, they don't have to analyze expressions of feelings typical for their culture in order to learn about it. They sucked it up from the beginning. A really awesome poem might not even be that awesome to them, as it's normal. They don't have to understand it to understand the culture, they live it. Although I think that everyone should, if they want to use it as an argument.
The rest, I agree. Using culture as an argument against foreigners is not my favorite, but it's very common as it's easy, and superficial. Most people have no clue, really, what their culture is, what their values are. If you mention the good, mention the bad. Everyone knows that there's always something to work on - that doesn't invalidate the good, not at all, it's the progress on the bad that validates the good.
I do care a lot about culture. But mostly about the culture that I pass on. My culture, what I personally took from what has shaped me, what I added to it, what I shaved off it. My personal set of values and believes, based on how I was raised within that original culture of mine, altered by my experiences, what I believe to be worthy to represent and to pass on.
I live by a rule. "The word is not the thing". Sweet isn't a flavour, it is a word. Sugar tastes sweet, it is our senses that interpret it. Our behaviours. Naming something and having the same word for it, doesn't mean we actually have the same experience. In this way, the culture through words is an assumption that understanding of experience is the same. Isn't that damaging? You are assuming because we use the same word, we feel the same about the experience.
If the nature of culture is intrinsic, I would challenge the majority of twenty year old Finns to a test on the culture derived from their history, their literature, poetry. When they are spending their time living in a digital world of whatever they do, what do they know? Do you think people are born with local culture?
And this is why all culture dies. All of it eventually gets shaved off.
No, the opposite. I assume that we use the same word, but have different understanding of it. Superficially learning a language is not enough, hence the argument of non-translatable words. When we just translate in our head, we don't get a deeper understanding. As cultural foreigners, we need the other aspects such as poetry to understand the predominant culture of the area we live in. If we want to be a real part of the community that is.
No, they're raised by local culture. The digital aspect is valid, and has some influence and will have more influence but by bit, unfortunately. Some could say the culture is infused by indoctrination. And yes, they would probably do pretty good on those tests. Not in the specific "what does that line mean"? Part, but other things like idioms, symbolism and such, that we first have to learn, but they grew up with.
No, not all. The core remains the same, the core values. The behavior around those values is what changes. In my case, I tried to be more coherent with my values. In other cases, people become more incoherent with their values (the Neonazis you describe for example).
I don't think that culture is just that one thing, fix and unwavering. It's more like the planet earth. The superficie changes, even the tectonics float around, but the core remains for a long time, without addition nor substraction.