Idiom:
Not X, but Y <== X and Y should be parallel.
In this question,
because of the passive voice, the correct idiom is:
Not by X, but by Y.
An increased level of entrepreneurship in the metropolitan area was
brought about not by immigrants who
arrived in a substantial influx, which was the case in cities several decades ago, but adjustments to the
federal tax code that heavily favor the self-employed.
(A) brought about not by immigrants who arrived in a substantial influx, which was the case in cities
several decades ago, but
Wrong. Not by X, but Y <== wrong idiom.
(B) brought about not by a substantial influx of immigrants, the case in cities several decades ago, but
Wrong. Not by X, but Y <== wrong idiom.
(C) brought about not by a substantial influx of immigrants, as was the case in cities several decades
ago, but by
Correct. Idiom:
Not by X, but by Y. (D) not brought about by a substantial influx of immigrants, which was the case in cities several
decades ago, but was brought about by
Wrong. Very wordy. We don't need to repeat verb in the second part "but was brought about by.."
(E) not brought about by immigrants who arrived in a substantial influx, the case in cities several
decades ago, but by
Wrong. Parallelism problem: not brought about by X, but [...???... ] by Y
Meaning problem: a substantial influx of immigrants (the whole influx) # immigrants who arrived in a substantial influx (some people who arrived in an influx).
Hope it helps.