For a modern example, I've lived 15 years in Britain (i.e. the UK) and I'm legally resident in the country but I am not, in any meaning of the term, "British".
Perhaps there is a confusion between the term "spartan" (which you render with a small "S") and "Spartiate"? In Greek there is only one word, "Σπαρτιάτης" ("Spartiates"). I believe the use of the term "spartan" to distinghuish between citizens of Sparta and e.g. helots or perioikoi, is a modern habit. As in very modern- as a young Greek I was fascinated with the ancient era and so I read a lot on ancient Greece but I don't remember such a distinction anywhere in the (Greek-language) sources I studied.
Indeed, if I try to translate "spartan" in Greek so that it sounds like a different word to "spartiates", I'd have to say something like "Σπαρτινός". But that is not a word I've ever heard spoken in Greece, nor, dare I say, has anyone else.
And Sparta has a higher share of helots than any other polis. If you are a woman in Sparta, almost sure that you are a helot (as many rights as a cow). Remember also that Spartiates regularly went to war against the helots, and Plutarch even remarked how cruel and harsh they were with the slaves.
So Sparta was arguably at least as bad as any other polis to be a woman unless you win the birth lottery as a spartiate.