When his wife committed suicide, Shelley was denied custody of his chi

OFFICIAL EXPLANATION





• Split #1: HIS belongs with one item or all

In a list, a word that applies to all items on the list must either be used only before the first list item or be repeated before each list item.
The first his is placed in the non-underlined portion of the sentence.

Shelley was denied custody of his children on the grounds of
(1) HIS X, Y, and Z
or
(2) his X, his Y, and his Z

Words that GMAC likes to fool around with in this context are usually
→ articles (the, a, an)
→ determiners (this, these)
→ possessive pronouns (his, hers, my)
→ prepositions (at, in, for), and
→ split verbs (to dance, act, and sing)

Option B uses his before the first and third items.
→ In order to maintain parallelism, his must also come before the second item.
Option C uses his before the first and second items; his should also come before the third.
In both (B) and (C) the list consists of three straightforward, parallel nouns: the problem is the uneven use of his.

ELIMINATE B AND C

• Split #2 - In a list, X, Y, and Z must be similar parts of speech and perform the same logical function

In option A, the list items are not similar parts of speech and are thus not parallel.
→ his atheism (HIS + noun)
→ because he was immoral in behavior (no HIS) (+ noun clause with a subject and verb)
→ his radical politics (HIS + noun)
because he was immoral in behavior is a noun clause (a.k.a. a substantive clause or a nominal clause), which you can read about in this post, here.
→ a noun and a noun clause are not similar parts of speech

The list items in option E are not parallel, either.
→ being an atheist (gerund phrase) (verbING phrase)
→ immoral in behavior (noun + prepositional phrase)
→ having radical politics (gerund phrsae)

Nothing is wrong with being and having. Nothing.
The problem is that the second item is not a gerund (verbING) phrase: being, immorality, and having are not parallel.

Eliminate options A and E

The correct answer is D
Correct: his atheism, his immorality, and his radical politics

Notes

Most of the time, GMAC chooses not to repeat an article or possessive pronoun before each list item but rather to let the first mention "distribute" to the other items.

vijk , you are mostly correct—GMAC patterns suggest that the repetition of his in option D is unnecessary.

I suppose that I would remember, first, that we are not trying to find a perfect sentence. We are trying to find four wrong answers.

Second, I saw a recent official question in which some element just like the word "his" in this question was repeated before each item.
I was surprised.
I even emailed the question to myself. I cannot find it at the moment. I will.

I gave you all this question because I saw a recent similar official one.

I understand your point.
Because I always have my eye on the big picture, I also understand that certain GMAT companies and tutors present certain SC patterns as inviolable.

The patterns are not inviolable.
The companies and the tutors ought not teach so rigidly, though perhaps not doing so would be at the expense of the sanity of their target audience.

COMMENTS

GowriPrakash, sydqur, shivangishar, vv65 , and praveena1234 , welcome to SC Butler.

I am glad to see all of you: newcomers, occasional visitors, Butler regulars, and veterans.

The standing invitation to all non-expert aspirants is always in effect: please feel free to post a reply.

These answers are good—but not quite explained fully. Or they miss the mark a bit.

Try to explain as if someone who were just learning about parallelism were reading your answers—because soon they will be doing exactly that.

Stay safe, everyone.