In terms of translation, I agree with the existing answer more or less. そうあってはいけないとみんなで決めて、それはそうやって言葉にされる前から自然と理解できていたことだったから translates: We agreed that we should not be so, and that (we should not be so) was naturally understandable before it (the agreement) was put to words that way, so...
Note that I haven't read the light novel which seems available online.
If there is no concrete description of how 'we all agreed', then a reasonable interpretation is that そうある refers to the general attitude of which セオ's harsh utterings were an expression. That is, in the story's world 86 is the discriminated-against kind and the officer girl is from the(?) discriminating race. But generally it is not a fault of any individual, and そうあってはいけない means 'we (86s) should not get emotional about being discriminated against (towards any individual person)'.
I guess the following sentence (another 86's words, later in the same page) should be relevant:
『それは不要です。別にあれが我々の総意というわけではありません。この現状を貴女が作りだしたのでもなければ、貴女一人の力で撤回できるものでもないということはわかっています。貴女には不可能なことを、しなかったと責められたからといって気に病む必要はありません』
Edit:
I'm uncertain how valid the following are, but just some hints.
To be and to exist overlaps in English as well: I think, therefore I am.
ある can mean a variety of 'being' including to be, to exist, to live, to stay. In particular, continuative form (連用形) + ある can mean to stay in the state (described by the word in 連用形).
For example: 彼女はきれいである She is beautiful. Here である can be treated simply as is, but in 彼女はきれいでありたい She wants to stay/become beautiful, it looks more natural to see it as きれいで + ある, where きれいで is a continuative form of きれいだ (or きれい+だ). It means the same as 彼女は美しくありたい, where 美しく is a continuative form.
Now for そうある/そうである, the former is used more often as そうありたい, そうあろうと etc while そうである can be used in this plain form. そうある is read as to exist/be (in) that way, just as きれいで 'modifies' ある. I.e. そう is an adverb describing how the subject is. On the other hand, である in そうである sounds as a copula (the subject is that). In a sense, this means the 'copula-ness' of だ in そうだ/きれいだ are different. The former is somewhat stronger. I guess it could have something to do with accepting 形容動詞 (see 形容動詞への対応).
See also: Can the である copula be explained as で (particle) + ある (to exist), i.e. "to exist in the form of ~"?