This is one of the most complex topics found within any nation that is primarily composed of multiple generations of immigrants coming from all over the world (including, the USA, Canada, Australia, New Zealand, Great Britain, etc.). There's a need to acknowledge the immigration, native assimilations, and/or kidnappings that led to the arrival of previous generations, while, simultaneously maintaining an awareness of our current commonalities within our larger, national society. Few people of any nation know the origins of all of their ancestors, going back six or more generations.
Those of us who have had family members living within our current nation for many generations are often a complex mixture of ethnicities, religions, and races. At earlier times in American history, Germans, Irish, Polish, and other impoverished Caucasians who arrived on American soil were treated with antipathy and hatred, regardless of the color of their skin. Usually, it was their religion and/or accents which made their cultural/ethnic/racial origins overt enough for them to be discriminated against.
With enough generations of intermarriage between ethnicities/races, the lines between them become so blurred as to be completely meaningless. I happen to have ancestors from several western and northern European nations, in addition to a great-great-great-great grandmother who was full Cherokee. Looking at me, no one can see my Native American heritage, nor clearly identify which Caucasian nations my ancestors originated from, nor when they arrived on USA soil.
As I have no doubt that some of them had slaves, at some point or other (as they all came from the southern parts of the USA, prior to branching out across the USA), it's possible that I may have some African genetic roots that I'm not aware of, as well. On top of all of that, I converted to Judaism, several years ago. So, no one can accurately "describe" my ethnic/racial lineage, simply by observing me in any given setting. Yet, if I'm forced to fill in some sort of racial/ethnic "box", I'll either put multi-racial or Caucasian down, depending on my mood - knowing it really doesn't matter, in my case, as I'm an American blended from both native and immigrant roots that I'm long separated from. While I'm not racially/ethnically Jewish, I'm culturally and religiously Jewish, as well, but no one really cares - not seriously - apart from those who are close to me.
I recall my maternal grandmother telling me about how her family (which was of major German heritage) had to lie and cover up their ethnic background, during both of the world wars, due to the constant fears of treasonous Germans, on U.S. soil. I'm uncertain what the exact circumstances were that led to my Cherokee ancestor marrying a southern, Caucasian man - whether it was a voluntary situation or a violent/forced family scenario. I'm unable to determine even whether she lived before or after the "Trail of Tears" occurred, nor which state(s) they lived in, while raising their family.
The reality is, that within the USA, many people are multi-racial without knowing it and/or admitting it. It takes a great deal of time, money, and energy to thoroughly and accurately research the facts about one's ethnic/religious/racial heritage and even the so-called "facts" may be lies, put into play to cover up dark or uncomfortable family secrets, including adoptions, illegitimate children, kidnapped offspring, incestuous links, untimely/criminal deaths, rape-related births, extra-marital affairs, long-term institutionalizations (in workhouses, psychiatric asylums, TB sanitariums, blind/deaf/developmental disability special schools, etc.), foster children, imprisonments, and so much more. So, one's facial features, skin color, accent, current religious practices, and so much more are unlikely in highly immigrant-supportive nations, like the USA, to tell the onlooker much of anything of importance about the ancestry of the person they are viewing/talking to.
Many adopted and foster children have no idea what their own parents' ethnic/racial/religious roots were, let along relatives from more distant generations. A friend of mine has a mother who is ethnically Korean, but was born and raised in Japan, before immigrating to the USA. Meanwhile, her father's family came from multiple European nations. When people look at her, they know she has some sort of oriental background blended with Caucasian features, but it's all truly meaningless, when there are so many different layers of movement between nations and cultures/sub-cultures over generations, along with inter-marriage between cultures, races, religions, and ethnicities.
While this subject technically is quite meaningless, based on the huge amount of inaccuracies that most individuals have about their own ethnic/racial lineages, let alone those of others (due to the general lack of interest in exploring geneaological data, amongst a well-known long-term history of societal "cover ups" of ethnic/racial/religious facts), some people treat the entire subject with deadly earnestness. They are so intense about it, generally, because they hold some belief that one or more ethnic/racial groups are, inherently, superior or inferior, to others which is entirely ridiculous and bigoted.
Racial, religious, and ethnic origins wouldn't matter on the large scale, if the vast majority were equally comfortable with all ethnic, racial, and religious groups, which is tough to be, considering how many there are in the entire world.
As an RN and certified teacher, I've provided health care and educational opportunities to individuals of all ages, ethnicities, races, religions, language skills, literacy skills, educational levels, ability levels, socio-economic backgrounds, genders, sexual orientations, and family/living situations, because that's what it means to be an "American RN" and/or "American Teacher". Being an American means being prepared to interact with people who may be fairly familiar with conventional assimilated American customs, language, and traditions, right along with engaging with those for whom all of these dimensions of American lifestyles are unfamiliar.
I believe that all who consider themselves to be genuinely "Americans" need to be equally prepared to interact with both natives and immigrants of diverse backgrounds and experiences. That's what the USA has always been and always will be - an immigrant and native-blended nation that continues to mix, merge, learn, and explore new lifestyles/foods/customs/beliefs/etc. in a way that makes our country unique - as the first "democratic-based" nation on the planet. To be an "American" means to be willing to blend and mix with people whose religious beliefs, accents, facial features, skin tones, family ancestry links, educational exposures, income levels, skin/eye/hair colors, and lifestyles are both similar to and different from one's own.
I believe that those who are unwilling to tolerate the diversity inherent within this nation are not now Americans, regardless of what their passports and/or birth certificates may say. Their narrow-mindedness makes this the wrong country for them and they need to move to a place where they can feel more comfortable - if any other nation is willing to take them, that is. It's far better to be an ex-pat than to be a fake American or American in name only, in my experience.