E.G.

You can correctly say of an undocumented person that she is not a legal citizen, i.e., isn't considered a citizen by the US government, doesn't have a US passport, isn't allowed to vote, can't run for political office (or most political offices, anyway), might be deported, etc. But most undocumented people are citizens, I think, despite a lack of legal recognition of their citizenship.

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If you want to argue against my view, I think your best strategy will be via some version of the following theory of citizenship:

Citizenship is a mere legal construction: An individual S is a citizen of a given country if and only if and because S is a legal citizen.

If this theory were true, then it would follow immediately that undocumented people aren't citizens.

However, consider the following argument:

Citizenship isn't a mere legal construction
(1) If citizenship is a mere legal construction, then citizenship is not morally significant in itself.
(2) Citizenship is morally significant in itself.
Therefore, citizenship is not a mere legal construction.

In my opinion, (2) is true. Here is an argument. We have certain cooperative obligations to our fellow citizens. In particular, we owe it to our fellow citizens to work together with them to create, maintain, and steer a political system that governs us as equals and serves certain important interests that we have in common. These cooperative obligations, I think, spring from the relationships that fellow citizens have to one another as fellow citizens. And this, I think, requires that the relationship of one fellow citizen to another has the moral power to generate these sorts of cooperative obligations. And I don't think that that relationship would have that moral power if citizenship weren't morally significant in itself. So, I conclude, citizenship is morally significant in itself.

I also believe that (1) is true. In general, mere legal constructions are not morally significant in themselves. True, we often have good reasons to care about mere legal constructions (e.g., you should usually pay attention to which areas are no-parking zones; and facts about no-parking zones are mere legal constructions) but the moral significance of mere legal constructions is always derivative and never intrinsic.

So, I think, the theory of citizenship according to which it is merely a legal construction is not true.

What I would say instead is that legal citizenship is a mere legal construction. And I do not think that legal citizenship is unimportant. Legal citizenship is the way that the state recognizes and affirms the independent reality of a person's citizenship. When someone goes through the naturalization process, for instance, and there is a ceremony where they are declared a citizen, etc., this does not have the effect of turning a non-citizen into a citizen, but it still does have an effect: it turns a citizen who lacks legal recognition of her citizenship into a legal citizen.

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I think the best theory of citizenship will be along these lines:

Citizenship is membership in a political society: An individual S is a citizen of a given country if and only if and because S is a member of that country's political society.

This view makes sense of the intrinsic moral significance of fellow citizenship. The fact that you and I are both members of the same political society seems like the sort of fact that could explain why, and make it the case that, I have certain cooperative obligations to you that I don't have to others.

Further, I think it is the case that most undocumented people are members of our political society. This, I think, is obviously true. But I will mention two objections that someone might make.

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First objection: You might say that undocumented people aren't members of our political society because (i) in order to become part of a country's political society, one must be invited by that country's government to join; and (ii) because undocumented people haven't gone through the naturalization process, they have not been invited by the American government to join; so, undocumented people aren't members of American political society.

But people who are born in the USA are not usually invited (formally or otherwise) by the American government to join our political society, but they are members of our political society nonetheless. So, (i) is false. And in general, it is not plausible that one must be invited to join a society in order to be a member of that society. Consider a household, which I take to be a kind of small, non-political society. If someone has been living in your house for years, doing things that members of a household do (e.g., they do chores, pay rent, sleep in one of the bedrooms, park their car in the driveway,…), then they are a member of your household, even if no invitation to join the household was ever made.

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Second objection: You might say that undocumented people aren't members of our political society because (i) in order to be part of a political society, one must be actively involved, politically, in that society; and (ii) undocumented people do not vote and do not participate in public political discourse; and (iii) voting and participating in public political discourse are the only ways for someone to be actively involved politically in America's political society; so, undocumented people aren't members of American political society.

But first of all, (i) is false. If (i) were true, then babies and politically apathetic adults who don't vote wouldn't be part of our political society, but they are. Also, (ii) is false. True, undocumented people don't vote, but many are participants in public political discourse (e.g.). Also, (iii) is false. One can be politically involved without ever saying a word and without ever casting a vote. For example, undocumented people are used as pawns by politicians (e.g., Trump stokes irrational fear of undocumented people to manipulate people into voting for him) and this is a form of conscripted political involvement in America's political society.

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Broadly, I don't know of any good reason to deny that most undocumented people in America are part of America's political society. Also, I don't know of any good alternative to the view that a citizen just is a member of a political society. So, it seems to me, we should just say that most undocumented people in America are American citizens.

My thinking on these issues is largely derivative of and indebted to the ideas of Sue Donaldson and Will Kymlicka in their book, Zoopolis: A Political Theory of Animal Rights, although it is not clear to me whether they would affirm the theory of citizenship given above or endorse the argument I've given, though I do believe they endorse a closely related view (I will need to go back and check what exactly they say).