In the high-profile Senate race in North Carolina, neither Senator Kay

I marked 'D' because I felt this option is grammatically correct as we can have cascaded modifiers(i.e. one after the other).
Here modifier ' the Republican challenger' modifies Thom Tillis while the modifier "who is Speaker of the North Carolina House" modifies the Republican challenger. This construction is grammatically and logically correct.
But there's a catch. I think there is a slight meaning change in 'D' as this option talks about a republican challenger while 'E' rectifies this meaning change via usage of 'her'. Even the question stem points to 'her' challenger not just any challenger(because republication party might have other candidates as well).
Option 'E' preserves the intended meaning and is also grammatically correct.

Doesn't option E suggest that Thom Tillis is her Republican Challenger and HER Speaker of the North Carolina House?

I think it creates some ambiguity because we can understand it with both the meanings "Thom tillis is her Republican Challenger; Thom tillis is a Speaker of the north.." and "Thom tillis is her republican challenger; Thom tillis is her speaker of the north carolina house".

The use or implies singular, therefore have is incorrect. So we can eliminate A, B, C

Between option D and E:
Thom Tillis is:
1. Republic challenger of Senator
2. Speaker of the North Carolina

In option D the Republican challenger seems correct, but use of back to back modifiers in continuation is incorrect.
Option E corrects this by using and for the 2 modifiers

In the high-profile Senate race in North Carolina, neither Senator Kay Hagan, who is the Democratic leader, or Thom Tillis, who is her Republican challenger and Speaker of the North Carolina House, have released recent campaign fundraising figures.

A. who is the Democratic leader, or Thom Tillis, who is her Republican challenger and Speaker of the North Carolina House, have
B. the Democratic leader, and Thom Tillis, her Republican challenger who is Speaker of the North Carolina House, have
C. who is the Democratic leader, nor Thom Tillis, who is her Republican challenger and also Speaker of the North Carolina House, have
D. the Democratic leader, nor Thom Tillis, the Republican challenger, who is Speaker of the North Carolina House, has
E. the Democratic leader, nor Thom Tillis, her Republican challenger and Speaker of the North Carolina House, has

Could someone please confirm whether "D" is totally wrong or it is just inferior to "E"?

I want to know whether the usage of cascading modifiers such as in "D" is aceptible.

D is wrong.
We have two modifiers modifying same thing.
This gives a list of two modifiers
Remember since you have a list you need to introduce AND to separate the items.
I hope I am clear as well as correct

OFFICIAL EXPLANATION

This sentence tests both verb tense and your understanding of the common constructions (neither…nor, not only…but also, etc.). One fairly easy decision point is the “neither…or” and “neither…and” in answer choices (A) and (B). Those are both incorrect so you should move to (C), (D), and (E), which all contain the proper “neither…nor.” When using “neither…nor” or “either…or”, the rule for subject-verb agreement is that you agree with whichever noun is closest to the verb. In this example, that noun is “Thom Tillis” and you should have a singular verb. In (C) the “have released” is plural so you can eliminate that choice. In (D) the subject verb agreement is correct but the modifiers following “Thom Tillis” are not parallel and illogically “stacked” on top of each other. Only (E) uses the proper “neither…nor”, the proper modifier structures, and the proper singular verb “has released.” Answer is (E).

GMATNinja, I need help with the answer choice between D and E. Why (D) is incorrect?

The only thing that differs between (D) and (E) is the structure of the modifiers.

In (D), Thom Tillis is described by two consecutive modifiers: "...Thom Tillis, the Republican challenger, who is Speaker of the North Carolina House, has..." Veritas is basically arguing that it's inelegant to stick two modifiers right next to each other like this. Fair enough: the two modifiers are describing the same thing (Thom Tillis), so they should be parallel, and separated by "and."

And that's exactly what happens in (E): "...Tillis, her Republican challenger and Speaker of the North Carolina House, has..." And arguably a small bonus point in (E) for adding some extra clarity by calling Tillis "her Republican challenger" -- but I don't think that's a big deal.

Don't overreact to the issue in (D), though: I don't think the GMAT would argue that it's always wrong to have two modifiers in a row like this. It's just that (E) is a better, clearer alternative in this case.

Isn't 'her' in option E ambiguous?
Can't 'her' refer back to both the names before it??

Thanks in advance.

E is the correct answer

First decision point: idiomatic expression Neiter...nor....Eliminate A&B
Second decision point: the verb must follow and agree with the noun after "nor" ...here it should be singular "has"..eliminate C
D&E left ...E is more efficient and clear than D

Hi Nitish,

nor Thom Tillis, her Republican challenger and Speaker of the North Carolina House,

In this "her" cannot refer to any other noun, because it is part of modifier and this modifier is modifying noun Thom Tillis.

Hence the usage in E is correct.

Thanks. Hope it helps!!

meaning test on sc is about
logic, clear and not redundant.
look at choice D, is this clear meaning. no. republican challenger of who. E show that the meaning here is clear. D is not clear meaning

Yeah right. D is grammatically correct because technically there is no difference between "Thom Tillis" and "the Republican challenger" as the latter one is an appositive. Which means whether "who is Speaker of the North Carolina House" modfies "Thom Tillis" OR "the Republican challenger", it is one and the same thing.