Here are a few ways in which to rewrite this sentence. However, I would say that the sentence as it stands is perfectly fine.
If you want to emphasize the deaf ears, then you can say: "Deaf ears characterized the people of Birmingham as they heard the sermons of Martin Luther King Jr."
Here is another variation, which takes some liberties: "As the people listened to the words of Martin Luther King Jr., they heard only superficially as it did not move them to action."
Here is another variation with some more liberties. "It was as if Martin Luther King Jr. was preaching to himself, as his words fell on deaf ears in Birmingham."
Here is one last variation, which is more poetic: "Deaf were the ears of those of Birmingham, as they did not really hear the preaching of Martin Luther King Jr.
I will attach two works that deal with Martin Luther King's letter.