Ironically, Carver's precision in sketching lives on the edge of despair ensures that his stories will sometimes be read too narrowly, much as Dickens' social-reformer role once caused his broader concerns to be (i) _______.

The idiomatic expression here is "much as" which indicates parallelism or similarity in the two ideas connected by "much as".

First Idea: Ironically, Carver's precision in sketching lives on the edge of despair ensures that his stories will sometimes be read too narrowly
Second Idea: Dickens' social-reformer role once caused his broader concerns to be (i) _______

Really speaking it is only the part highlighted in blue that one needs to pay attention to, as they are parallel. They represent the (similar) outcomes of two different things.

Carver's precision in sketching....... LED TO his stories being read narrowly.
Dickens' social reformer role.... LED TO his broader concerns to be

The idiomatic phrase "much as" insists that both the parts convey the same idea. So the second part should also proclaim that Dickens' social reformer role caused him to be read narrowly or his broader concerns to be ignored.

The word from the list of choices is ignored.

there are 2 strong candidate answers here. Ignored and diminished. In the first case, those who enjoys Carver's work will read it narrower than it should be due to his mastery of depicting lives on despair. They thought the works will always be related to the norm of his work, which is despair. Similar to this, due to Dickens' political activity in social reformer caused public to deem his concern narrower than it actually is.

Now lets get to the answer choices. If we put diminished in the blank, it would change the sense of the context as in this case, it will be Dickens himself that renders his concern to be narrower. In other hand, if we put ignored, it is clear that it is someone else that ignore the concerns. So ignored is the best answer.