The doctrinal dispute resulted in the dismissal of the president of th

The issue is parallelism (he's charged with 2 things). Both B and D have ambiguous interpretations of what those two things are.

Because of the repeated "with" in A, we are forced to realize that the sentence up to "charged" is common to both endings.
(A) ...charged: (1) with teaching false doctrine and (2) with administrative misconduct

But (B) could be interpreted as:
...charged with teaching false: (1) doctrine and (2) administrative misconduct
...charged with teaching: (1) false doctrine and (2) administrative misconduct
...charged with: (1) teaching false doctrine and (2) administrative misconduct
The last interpretation is correct, and the others are a little silly (how do you teach false administrative misconduct, I wonder?), but since another choice is more clear you must go with it.

(D) has similar possible interpretations, plus the awkardness of using "teaching" as a noun.