My contention is that this is such a fuzzy term that it doesn't really mean anything, and that most people who use the term would struggle to actually clearly articulate what is and isn't part of "their" culture.
Merriam-Webster defines culture as:
Merriam-Webster wrote:a : the integrated pattern of human knowledge, belief, and behavior that depends upon the capacity for learning and transmitting knowledge to succeeding generations
b : the customary beliefs, social forms, and material traits of a racial, religious, or social group; also : the characteristic features of everyday existence (as diversions or a way of life) shared by people in a place or time <popular culture> <southern culture>
c : the set of shared attitudes, values, goals, and practices that characterizes an institution or organization <a corporate culture focused on the bottom line>
d : the set of values, conventions, or social practices associated with a particular field, activity, or societal characteristic <studying the effect of computers on print culture> <changing the culture of materialism will take time — Peggy O'Mara>
None of these definitions suggest culture applies exclusively to "the nation" as a thing. There are subcultures all the way down to the smallest possible group. My family has learned patterns of knowledge, beliefs and behaviour that distinguish us from other families in the same neighbourhood. A bunch of skater friends who do tricks in the central business district share their own culture, which is clearly distinguishable from the culture of all the other people that walk past them on their way to and from work. In fact, chances are that those skaters would share a lot of knowledge, beliefs and behaviour with skaters on the other side of the world. Hell, even NSG has a culture of sorts, which ties regular posters together no matter which country they are from.
So usually when I ask people to define their culture, they go to language, religion and certain customs and rituals. Language is one thing - but given that there are a bunch of countries that have several languages, that seems to be problematic. Is there no such thing as Swiss culture, because Switzerland can be divided into subsections by language? And while the skaters are perfectly able to communicate with the office workers in the common language of the country, they do not use the same language when talking to one another - slang, memes and inside knowledge form part of their subculture and are used to reinforce it.
So, because a lot of the time these discussions end up about immigrants who "don't assimilate into the nation's culture", people often go to religion. But that's just demonstrably false - there are very few countries in the world with a single religion so dominant that this makes sense. Germans have many religions: There are lutherans, catholics, plenty of atheists and many others. Which one is more German than the other? And besides, many countries have people with these religions - no one would reasonably say "I'm catholic, therefore I am German".
So then you get to thinks like "do they celebrate the same holidays?", which is really just the same thing as religion in the majority of cases, and at any rate seems a fairly petty way of defining a national culture. So share rituals? Australians for example might point towards things like Anzac worship as being a part of their national culture. But I know plenty of Australians who don't make a big deal of it - some of them even worry about whether it is a good thing. So are they not real Australians?
One last thing people sometimes bring up is particular character traits or ways of behaving. Australians might say "mateship" is an Australian trait. Germans might say "punctuality" is part of being German. But that again strikes me as a really bad way to distinguish a nation of millions. Not only are not all Germans punctual or all Australians mates, but lots of people outside those countries exhibit those traits too.
So basically, I'm left with the impression that few people if any actually have working definitions of their national culture. It's a kind of diffuse "I'll know it when I see it" concept. That throws the door wide open to abuse (just look at the Islam in Germany thread for examples out the wazoo) and makes it incredibly difficult to have reasonable discussions about topics that touch on national culture. It also makes it incredibly difficult for newcomers to a country to know what they have to do in order to "assimilate" sufficiently for people to stop saying that they're not trying hard enough.
So am I wrong? And if so, how do you define the culture of whatever country you consider yourself part of?