である, な, and some instances of の are all "modifier" versions of the copula verb です. When you want to say "the building that I see from my window", you use the plain form 見る in 窓から見るビル. If you're saying "the books that I read lately", the plain form 読む in 最近読む本. So when you use a verb to modify a noun (or noun phrase), the pattern is [phrase ending with a plain-form verb] + [noun or noun phrase].
Now, the plain form of the copula です is だ - but as an exception to the above pattern, you can't use it as a modifier - instead, you use の. For "John who is a doctor", you don't say 🚫医者だジョンさん🚫 - instead you would say 医者のジョンさん. "The tree that is her home" is 彼女の家の木 - except that this could also mean "the tree of her home", or it could even refer to the wood from which her home was made.
Except, when the final word before the copula is an adjectival noun, you use な instead of の. "(The) Mary that loves candy" (or "Mary, who loves candy") is キャンディーが好きなメアリー. And of course you also use な with regular nouns in the specific case where you follow it with んだ, のです, or the like.
Now, である. である is equivalent to だ, except that (a) it is used in place of だ or です in "literary plain form", a style often found in books, that uses plain verb forms, but with just a dash of extra formality thrown in; and (b) it can be used as a noun-modifying verb, without modification. In this style, その本だ becomes その本である; and 医者のジョンさん (recall: "John who is a doctor") could be 医者であるジョンさん.
However, uses of な would typically stay the same. You'd still have キャンディーが好きなメアリー; you would not have 🚫キャンディーが好きであるメアリー🚫.
And, of course, the use in more typical Japanese of の as the "modifier" form of だ, can lead to confusion. Ordinarily, いもうとちゃんの本 means "My little sister's book" - but what if we're in a story in which an evil witch has transformed your little sister into a book? Even though the context makes it clear that "My little sister, who is a book" might conceivably be a possible interpretation for that phrase, it's still just too far from a "normal" reading of it, and a Japanese reader would likely still assume it's "sister's book". In such a case, the use of である then can also serve the purpose of disambiguating between "the Y that is X" and "X's Y". いもうとちゃんである本. For the "the tree that is her home" example, in reality I'd expect to see that as 彼女の家である木 as well, due to the same kinds of ambiguities, mentioned previously.
And this brings us to the explanation of 社会人である限り. 社会人 is not an adjectival noun, but just an ordinary noun, and so the rule would be to use の to mean "The constraint that is [being] a member of society"; except that 社会人の限りは would make it "the constraints [or limits] of society members" instead, referring potentially to limitations that members of society have, rather than a limit that membership in a society demands. So である is used to give it more of the former flavor than the latter.
