It’s somewhat problematic to talk about Canada at all.
First, Quebec. Around 23% of the population of our loose confederation speak a separate language, live in a province that considers itself sovereign, and range between outright hostility and indifference to the rest of the country. They constitute a separate nation whose tragedy is that they lack a fully independent state. And most of us in the rest of the country are incapable of conversing with them and are more or less ignorant of their culture. If you disagree with that, tell me your three favourite Québécois teleromans from the last ten years, and confirm that you consider Tout le Monde en Parle to be must-watch TV. Let’s at least agree that for the purpose of this thread, our country doesn’t include Quebec.
Second, the rest. Us. What can you say about a society whose seminal political treatise was entitled, “Lament for a Nation”? English Canada is perhaps the only society on the planet devoted to the belief in its cultural non-existence. Unlike our Québécois co-passport holders, we refuse the possibility that we have a shared, collective culture that binds and unites us. Quite the opposite - English Canada’s dominant narrative is our collective culpability for historical and current injustices to aboriginals and a multiplicity of immigrant or gender/orientation groups, and the proper lack of primacy of any one common culture over the astonishing number of plants in our multicultural garden. English Canadians are perhaps the only people on the planet who believe that asserting a collective identity would be a morally wrong form of aggression. We tell ourselves ad nauseum that diversity is our strength because we have nothing else. Perhaps that makes it easier for immigrants to come here than any other place. I think Nino Ricci once wrote that Canada was more of a comfortable hotel than a real country. I haven’t been able to locate the quote, so it might have been another novelist. In any event, this hotel doesn’t demand anything of its guests, nor does it provide them with the sense of belonging that real countries confer on their citizens.
But perhaps something good comes of having meagre national identity. I travel a lot for extended periods, and as an English Canadian I’m struck by how at easily I can enter other cultures at least on a superficial level, how at home I can feel pretty much anywhere in the developed world. I mourn our inability to create a national sense of belonging. But it’s a big, wide, beautiful world, and with our bland inoffensiveness and Zelig-like lack of a cultural core, we English Canadians (I apologize if that term gives offence) are perhaps uniquely positioned to enjoy it. Something gained for something lost.
I must say, I beg to differ w/this point of view in many respects.
By way of background, my family is 1/2 Quebecois, 1/2 Scots-immigrant
In that context, I have grown up w/francophones, both those who settled in Toronto, but were still fluent French, and moved here from Quebec, as well as family remaining in Quebec, with the counterpoint of anglophones, I think i have some perspective.
I really do see this country as having a clear identity and one that easily differentiates from other countries, while being quite similar here at home.
****
First off, while Quebec certainly does have a distinct culture from English Canada, it relates culturally more to English Canada than France or needless to say, the U.S.
We so share common bonds in hockey and other winter sports, we do have many common historical frames of reference, most Quebecers, in my experience, do speak English, albeit this is less so outside the biggest urban centres.
Even before poutine became a thing in English Canada, we did share many culinary loves, and not only those borrowed from the U.S. or elsewhere.
In the not-yet post-PQ era, our politics aren't sooo far apart either. Quebec's welfare state is only modestly more robust than Ontario's; the differences w/the U.S. being vastly more clear.
While I certainly wouldn't overstate the level of French among anglo-Canadians, its much higher than many give it credit for; I know several families w/kids in French immersion, where demand vastly exceeds supply, and know few anglos w/no French at all.
In respect of broader English Canada, having traveled it much; I can tell you there is more in common between BC and Ontario, or Alberta and Newfoundland than any North-South connection (the U.S.)
****
Moving away from that to a different question.
What makes national identity?
I think people imagine more things in national branding and history than are true for the most part.
People imagine a clear US identity, yet NYC and Alabama have little in common beyond language (sort of) ....
I would argue the Bible Belt is almost its own country when compared with California.
Sure Canada is has 2 major linguistic groupings.
The Swiss have 3; I'm not clear that this is an insurmountable barrier to common understanding.
After language, what gives a nation identity? Common culinary history? Common Religion? Common beliefs in a political sense?
I would argue it could, in part, be any of these, though surely the latter is most important, along w/general disposition. (how we see ourselves in the world and relate to it)
I would suggest Canadians writ large see themselves and welcoming, open, and strong believers than merit and shared values make you Canadian, not your place of birth, or skin complexion, or accent.
I think there is a genuine sense of pride in that, which is shared by a majority across the nation, and I would also suggest that is, as yet, relatively unique in the world, giving us a different point of view
from countries that judge your name to belong to their culture or language, or your appearance; whereas Canada asks, more about the person, what they can contribute and much less about the superficial nonsense.
I'm not for a moment naive on the many shortcomings Canada faces in respect of the above, but having traveled a great deal, I can say I've never seen anyone else do it better.
****
Despite idiosyncratic differences throughout and within the provinces, I see common threads from respect for the Charter and our Supreme Court, broad acceptance of immigrants, yes, a love of hockey, poutine and fairly similar levels of social programs across the country.
****
Finally, stepping way back to the OPs point.
Certainly in urban Canada, and amongst my peer group, I can't imagine anyone thinking twice about whether someone is fully Canadian or equally Canadian, because of their colour of skin or where from or when they immigrated.
I'll share an anecdote on this; I know a young woman (late 20s) who happens to be black, and is from the United States. She spent some time in Toronto, for the first time, a couple of years back.
She was so completely stunned about how she felt she was seen or wasn't on our streets that it left very lasting and positive impression.
She spoke about how she didn't feel she stood out, or was judged for being black, and how she mixed w/friends and strangers from here of all backgrounds and didn't feel noticed or judged about it.
She compared this w/home, in the southern US where if she was in a majority white area, she felt very conspicuous.
That's one person's story, and surely there are others, including negative ones.
But I think it does stand out that in many respects, we aspire to be a country like no other, where you can love ramen, or fried chicken (or both) ; be agnostic, atheist or of virtually any faith; speak any language, have any complexion, and we're all good w/that, as long as you aspire to a value of tolerance, peace, freedom, and social conscience, we're all Canadian.