D：We can have “neither/nor” or “not/or,” but we can’t have “neither/or.”
In addition, the plural is off here: “parents’ divorces.” "Divorces" sounds like the parents had multiple divorces. While it might be the case that their parents had multiple divorces, it is unlikely, especially since the statement discusses a single divorce earlier on in the sentence: “ten years after the parents' divorce.”
(D) is out.

E：In general, any time you find yourself wondering whether a certain construction is allowed, you don't want to use it as a decision point. It's very easy to get lost deliberating over rules that don't actually exist.

In this case, "reasons that their parents divorced," isn't the world's most elegant phrase, but I'm not sure that it's WRONG, exactly. There's no concrete grammatical error. The notion isn't illogical. So I'm not getting rid of an answer choice on this basis alone. (Notice that there's no need for a preposition here. And while there are certainly hard-core grammar teachers who will insist that you can't end a sentence with a preposition, there's no consensus on this, so if I encountered this construction, I'd avoid using it as a reason to kill an answer choice.)

So instead, let's search for a more concrete error in (E). Take another look:

"...neither preoccupied with the reasons that their parents divorced nor even very curious about it"

What does "it" refer to here? The only logical referent is "the reasons," but "it" has to refer to a singular noun, so this is a definitive error. Now I'm perfectly happy giving (E) the boot.

The takeaway: Anytime you're unsure about a rule, accept the possibility that there might be no rule, and look for either concrete grammatical errors or problems with logic and meaning.