I'm going to get a bit theoretical and "wonky" here, but bear with me. Remember, government, both American and Japanese, is my area of graduate research.
The issue immigrants to Japan are dealing with is one of identity and the question is, "who is a member of society?" There are many facets of personal identity, including gender, sex, class, religion, educational background, and personal hobbies, but in terms of the aforementioned question, there are three we need to consider: ethnicity, nationality, citizenship.
In common parlance, we often equate nation with state as synonyms for country. We also sometimes talk about ethnic groups as being a nation. And these are just the English terms. Let me assure you, the Japanese terms are just as confusing for country or state, you have "koku" 国, for nation you have "tami" 民, and perhaps that's closer to the political science term. Then there's 民族集団 which is ethnic group, and you will notice it has "tami" as its root. So let's try to clarify which each of these things are... and do so in reverse:
Citizenship is having full legal rights as a member of a state. All states are nations, some states are nations and ethnic groups, but not all nations and not all ethnic groups have states. States have functioning governments and are generally (but not always) recognised as having such by other states. The United States of America and Japan both have internationally recognised functioning governments. They are states.
Nationality is having a recognisable membership or association with a group which has enough internal cohesion to be defined as an independent culture or civilisation. This includes aspects of language, religion, traditions and customs, philosophy, and shared sense of narrative, both historical (actual events) and fictional (shared stories). The United States and Japan are both nations. In addition, the United States is a nation OF nations. The Cherokee Nation, as an example, is a nation, but it is not a state, without getting into my feelings on the matter, the Cherokee Nation and other Native American nations are considered "ward nations of the American state." Another example would be Kurdistan. Kurdistan has "borders" in three different countries. Those countries are states, but Kurdistan is not a state. Nations often have physical areas associated with them, but they do not have to. National diasporas (such as the Jewish diaspora prior to the creation of the state of Israel) are still nations as long they retain enough internal cohesion.
This word is further complicated by the fact that in the United States we have terms like, "US nationals" and "foreign nationals." Foreign nationals is easy enough, it means anyone who isn't legally an American. "US nationals," however has a very specific meaning: someone who may or may not be an American citizen, but would be entitled to citizenship if certain qualifications are met. The best example of US nationals are those individuals living in "Free Associated States" like Saipan or the Marianas. They are US nationals, but they are NOT US citizens unless they move to the mainland US and request citizenship. They have limited tax liability and almost full legal autonomy. All US citizens are US nationals, but not all US nationals are US citizens. Under very rare circumstances, US citizens may be stripped of their citizenship and yet still remain US nationals. Some argue given the permanent consequences of a felony conviction, felons become a sort of quasi-citizen which operates much like being a "US national." These people are not considered stateless. This is a legal distinction and really has no bearing on the idea of nation as members of an internally cohesive culture. And not one which concerns our discussion of my views of Japan (but is very interesting!).
Finally, ethnicity is a combination of racial, physical, and cultural characteristics which identifies what a person's national origin is. National origin should not be confused with current nationality. Going back to the example of the Cherokee Nation, let's consider the descendants of Cherokee leader John Ross. John Ross was 7/8ths Scottish, only 1/8th Cherokee. His family's national origin was primarily Scottish. His family's nationality was (and still is), Cherokee. His family's citizenship was American (after the move to Oklahoma, and up to the present). Even today, the ethnicity of Ross's descendants is still primarily Scottish, their nationality is still Cherokee (and American), and they have United States citizenship.
So how does this apply to me?
My ethnicity is Irish. Both sides of my family come from the same area of Ireland. In fact, my mother's family actually took the land in County Cork from my father's family during the early part of the English occupation. We have lots of documentation. I can trace my family back to 1492. Ethnicity and national origin are very clear and unmuddled for me, as compared to many other Americans. I have an affinity for Ireland, but only in the most abstract of ways. I have never been there, and while I'll call myself "Irish-American" in terms of ethnicity, I am not Irish and have no wish to be Irish nor claim I am Irish. Despite the Irish Diaspora, I do not claim membership in the Irish nation.
I am a citizen of the United States. I am a recognised member of the American state with full legal rights. I obtained these by birth, and then later by reaching the age of majority. In addition, I have personally sworn an oath to protect and defend the Constitution of the United States which is what establishes the American state and enumerates those legal rights. I not only obtained US citizenship involuntarily, in my mind, I later accepted it voluntarily as a consenting adult with no mental reservation or purpose of evasion. This is why I feel I both cannot and will not give up my US citizenship.
Nationality is where we run into my conflict. I am certainly a member of the American nation. I speak American English, I'm an identifiably American Roman Catholic, I celebrate certain American customs, traditions, and holidays even when outside of the United States, my political philosophy is pretty much built on the ideas which went into the Constitution, and I understand and am part of a shared narrative with both historical and fictional elements. I couldn't stop being an American even if I lost my US citizenship. My experiences preclude it. However, part of being an American is also recognising that the American nation is not an exclusive nation. One of our shared narratives is the fact that members of the American nation may be members of other nations, and that's not only tolerated, but an inherent part of being a member of the American nation. You need not give up another nationality to become American, and if you are born an American, you need not stop being an American to take on another nationality.
I am, or in the process of becoming, a member of the Japanese nation, by my own understanding of what constitutes nation. In this case, "tami" or 民. Just as I can never stop being an American, I will always demonstrate some level of Japanese assimilation. I'll never be purely just a member of the American nation. Even if I left Japan right now, I have spent too much time speaking Japanese (and thinking in, and dreaming in Japanese), participating in Shinto and Buddhist religious services as a part of daily life, celebrating Japanese holidays, customs, and traditions even when outside of Japan, largely accepting Japanese views of social justice issues and civic duty which I apply to my overall political views, and learning about and communicating in a shared sense of narrative in Japan to ever "leave Japan behind."
And it is this definition of nationality which challenges Japanese understandings of nationality as inherently requiring identical ethnicity, one which my Americanness finds fundamentally flawed. And it isn't conscious. Most Japanese never even stop and think about it. It's part of the shared narrative, but no one says shared narratives need remain unchanged; in fact, one would argue that how internal cohesiveness is maintained in spite of changes in the shared narrative shows the true strength of a nation. It's slowly changing because of the amount of children being born in Japan with one non-Japanese parent, but resistance to the idea of Japaneseness without Yamato ethnic background at all is still pretty pervasive.
All that said, I've begun to address anyone who calls me a foreigner with:
I am not a foreigner. I am a Japanese resident.
Whether many ethnic Japanese cannot (or will not) conceptualise the idea of Japan being my home, the place I am now from or not, that doesn't change the truth of that fact. And how can anyone ever be a foreigner in their own home? I assert that such is a philosophical oxymoron.