Sentence Correction

Is c wrong because of restrictive "that"?

Not going into specifics of grammar, I believe that "shaped so smooth" is not correct in C.

I mean, "shape" and "smoothness" have no correlation. Basically the intention here seems to be to convey two things:

i) Wings are smooth
ii) Wings are shaped perfectly

Since the 1930's aircraft manufacturers have tried to build airplanes with frictionless wings, shaped so smoothly and perfectly that the air passing over them would not become turbulent.

(A) wings, shaped so smoothly and perfectly
(B) wings, wings so smooth and so perfectly shaped
(C) wings that are shaped so smooth and perfect
(D) wings, shaped in such a smooth and perfect manner
(E) wings, wings having been shaped smoothly and perfectly so

A and E: shaped SMOOTHLY
smoothly means performed WITHOUT DIFFICULTY.
Thus, shaped smoothly means shaped WITHOUT DIFFICULTY, implying that the process of shaping the wings is easy.
Not the intended meaning.
The intended meaning is not that the shaping PROCESS is smooth but that the WINGS themselves are SMOOTH.
Eliminate A and E.

C: are shaped so smooth and perfect
Here, smooth and perfect (two adjectives) seems to modify are shaped (verb).
An adjective cannot modify a verb.
An adjective must serve to modify a NOUN.
Eliminate C.

D: shaped in such a smooth and perfect manner
Like A and E, this option implies that the MANNER of shaping the wings is EASY.
Not the intended meaning.
The intended meaning is not that the shaping MANNER is smooth but that the WINGS themselves are SMOOTH.
Eliminate D.

The correct answer is B.

OA: Since the 1930's aircraft manufacturers have tried to build airplanes with frictionless wings, wings so smooth and so perfectly shaped that the air passing over them would not become turbulent.

The portion in green is an example of a RESUMPTIVE MODIFIER.
A resumptive modifier:

-- repeats a key word in the sentence
-- conveys additional information about that key word
-- often includes a that-clause
-- usually appears at the end of a sentence.

In the OA, the resumptive modifier makes it clear that so smooth and so perfectly shaped refers only to the WINGS, not to the entire airplane.
Check here for another example of a resumptive modifier:
https://www.beatthegmat.com/wasps-t38234.html