As far as the use of be is concerned, is the following sentence correct?
"When all past societies had separately prospered in peace within the local borders of their own solutions, now that they are melting in one big pot an impartial vision is due, whereby common grounds and differences be suitably understood."
Or is are instead of be the proper form?
My problem here is how to express the uncertainty of something that is not available here and now, albeit auspicable in the immediate future.
No, the sentence is not correct in modern idiomatic English.
When in doubt, simplify the sentence. This type of error only ever occurs in complex, overconstructed sentences, where less fluent speakers (including native speakers) can be tricked into forgetting simple things like agreement and conjugation. In this case, we simplify:
When all past societies had separately prospered in peace within the local borders of their own solutions, now that they are melting in one big pot an impartial vision is due, whereby common grounds and differences be suitably understood.
Now that they are melting, an impartial vision is due, whereby common grounds and differences be suitably understood.
Now a vision is due, whereby grounds and differences be understood.
Now a vision is due, whereby things be understood.
Things be understood.
Is "Things be understood" idiomatic in modern English? No--although it would have been in some archaic dialects, and on Talk Like A Pirate Day ("Aye, it be so").
The sentence could be corrected in many ways, while maintaining what was presumably the intended meaning:
...whereby grounds and differences can be understood.
...whereby grounds and differences are understood.
...whereby grounds and differences may be understood.
I think it is better to say:
"When all past societies had separately prospered in peace within the local borders of their own solutions, now that they are melting in one big pot an impartial vision is due, whereby common grounds and differences become suitably understood."
Since we are talking about a progression in time, become is a better word that be or are, which only describe the current state of things.
However, if this is a quotation, it might be a matter of writing style or locale dependent.
I see this "be" as present tense subjunctive .
I would argue that you could use 'be' as this text is referring to something not concrete and not set in either the present or the past, it implies doubt and uncertainty of a situation, 'an impartial vision is due' will that vision happen, if so when will it happen' we don't know, therefore this text could be seen as being in the subjunctive and not the indicative. https://en.wikipedia.org/wiki/English_subjunctive
Though there are other ways to express this uncertainty, one way has been noted with 'become' which implies change. It also could be done with be and a modal, but doing this might imply other contexts that we wish to avoid;
...whereby common grounds and differences should/may/ought to/need to/have to be suitably understood."
