IMO A.

Sulfur dioxide, a major contributor to acid rain, is an especially serious pollutant because it diminishes the respiratory system’s ability to deal with all other pollutants.
(A) an especially serious pollutant because it diminishes the respiratory system’s ability to deal
Correct.

(B) an especially serious pollutant because of diminishing the respiratory system’s capability of dealing
Because of should follow a noun....not a verb....

(C) an especially serious pollutant because it diminishes the capability of the respiratory system in dealing
Capabiltiy....in is unidiomatic...."ability to" as in A is better.

(D) a specially serious pollutant because it diminishes the capability of the respiratory system to deal
Specially is wrong...we are talking about quality of something...where especially is required.

(E) a specially serious pollutant because of diminishing the respiratory system’s ability to deal
Specially is wrong...we are talking about quality of something...where especially is required.

Just to distinguish between specially and especially

source: https://www.dailywritingtips.com/especia ... specially/

Especially or specially?

When it comes to the adjectival forms, especially should always be used. It modifies a verb, adverb or adjective and means “particularly” or “exceptionally”:

* His train was running especially late that day.
* We were especially happy to see you.
* I put the cake especially high.

Specially is becoming more common but still tends to sound rather informal, even a little child-like (“I drew this picture specially for you!”) There is a lot of debate around whether “specially” is appropriate in some cases, but if you want to be sure, stick with “especially”.

IMO answer should be A