At the beginning of his letter, Martin Luther King writes:

Injustice anywhere is a threat to justice everywhere. We are caught in an inescapable network of mutuality, tied in a single garment of destiny. Whatever affects one directly, affects all indirectly.

At the end of the paragraph, King limits his remark, in this instance, to those who live in the United States. However, the general implications of King's remark for people in relation to social injustice are clear. A tribal sense of justice and loyalty, based on in-group altruism and out-group hostility, is of no use. Those who object to injustice cannot fight it selectively. This is an easy statement with which to agree. If you think King is wrong, the strongest grounds on which to argue would be that injustice is so common that you have to be selective in fighting it.

The second statement in the question comes from the middle of the letter:

Shallow understanding from people of good will is more frustrating than absolute misunderstanding from people of ill will. Lukewarm acceptance is much more bewildering than outright rejection.

This is the conclusion of a paragraph in which King says that the principal threat he is addressing is not the open and extreme racism of the Ku Klux Klan, but the timidity and compromise of the "white moderate." This is still a common complaint among social justice activists, who find qualified, tepid acceptance of the need for social justice more frustrating than outright opposition. You may wish to argue that at least those whose acceptance is lukewarm have demonstrated that they are willing to listen, and they may be persuaded that a more robust attitude is required. Alternatively, activists who agree with King often say that the type of allies he describes are exactly the ones who slow the pace of change, allowing evil to triumph.