As for being the “citizen” of more than one state, I suspect that this question can come up in tax cases, when more than one state wants to ding you. I avoided tax law like the plague. Others with more familiarity with it can chime in. 
what about the idea that one apparently can cease to be the citizen of ANY state, temporarily, while that never happens to a citizen of a country (absent the special effort of renouncing citizenship).
By this question I mean when I move from state A to state B, there are residency requirements. I have to have a residence in the state, I have to live there for 30 days, have a utility bill, pay taxes, whatever the requirements are. It takes time to meet those requirements. I well and truly leave state A, change my address, notify the post office, do all the necessary things. I am gone-I no longer meet the requirements for residency in state A. It takes time for me to get my own place in state B. During the gap, I am not the citizen (or resident) of any state. But I always remain a citizen of my country. It seems that tenuousness indicates a reduced value or significance to being a citizen of a state.
Taxing also occurs based on what state you earned the money in. So a NH resident who works in MA will get taxed by MA on that income regardless of residency and the fact that NH doesn’t have an income tax.
Ten million stateless (in the international sense) persons would disagree.
Not to hijack, but losing your citizenship in any nation can and does occur. The nation you were a citizen of may cease to exist, for instance. So might a person born to immigrant parents within the boundaries in a jus sanguinis country (so the “birth country” considers the child a citizen of the parent’s nationality, not theirs) but the parents are citizens of a jus soli nation (so the parent’s nation doesn’t consider the child a citizen, it being born in another country.) And some countries have methods of stripping citizenship of their own citizens, which would render the victim stateless if they lacked a dual citizenship to fall back on.
Statelessness is shockingly easy to happen.
However simple it might be, this is not the rule. Citizenship for purposes of diversity jurisdiction is determined by domicile, not residence. Domicile basically means residence with the intent to remain (pdf) there; it can differ from residence most prominently in cases such as college students, prisoners, and military members.
Note that the application of the FFC to adoption judgments was only recognized by the Supreme Court this year. The S.Ct. has always applied the FFC more readily to state court judgments than to other public acts, which is generally why the FFC was never applied to marriages – those involve a state license but not a court judgment.
If you change your domicile from State A to State B, you have residency in State B at that point. The fact that State B may make you wait, or do other things, before being able to take advantage of your new residency (for example, for the purpose of claiming in-state tuition) doesn’t change that fact. You would be able to utilize diversity jurisdiction, for example. I believe that it is true you would always be able to register to vote in the new state as well without waiting.
For most purposes, you are a citizen of the last state or territory/district where you established a domicile. So as far as the US government and most state courts are concerned, you’re from DC.