Choices A,B,C, can be eliminated immediately because of the use of the antecedent "they," which appears before the comma. In this sentence, "they" is modifying "customs inspectors" not travelers.
Reread it like this: "No matter how patiently [TRAVELERS] explain their reasons for confiscating certain items, TRAVELERS often treat customs inspectors like wanton poachers rather than government employees." Does that make sense? NO. Travelers aren’t confiscating items from themselves.
Does this make sense: "No matter how patiently [CUSTOMS INSPECTORS] explain their reasons for confiscating certain items, [THEY] are often treated… wanton poachers rather than government employees."
This makes sense also, and ultimately this construction is correct: "No matter how patiently [THEY] explain their reasons for confiscating certain items, [CUSTOMS INSPECTORS] are often treated… wanton poachers rather than government employees."
There really isn’t a way for either of choices A, B, or C to be correct. (Antecedents can be deadly.)
Choices D and E are the only viable options. Honestly, both D and E are wrong to me. But D has the least sever problem, thus it is ultimately the answer. The biggest problem with D is the use of the word “were.” Doesn’t the use of this word here break the tense rule? “… Inspectors ARE often treated by travelers as if they WERE...” This construction is problematic! “Were” seems to change the tense of the sentence here, doesn’t it?
The glaring problem with E, though, makes it incorrect. Choice E leaves out the final “like” which is necessary to completely relate the idiom – not like X…. but [like] Y. That really is the only thing wrong with choice E.
I don’t agree with the argument that treated like is idiomatically incorrect. I’d like to add some complex deep reason for why I disagree with this argument, but I don’t have one. My reasoning is really quite simple. The phrase “treated like” is used regularly by writers for New York Times, as well the Associated Press. I know we don’t all always agree with the political ideals the Times seems to represent, but I think it goes without saying that the best writers in the world write for that paper; they don’t make mistakes. Ever. Hence, my rule of thumb regarding grammar: If it’s in the Times it’s right… that’s it.