What are implications of this statement for all people in relation to social injustice?

I'm not sure what statement you are referring to, but King asserted that standing up against all injustice, no matter what one's relation to the victim, and of doing so robustly, without constantly calling for moderation and compromise are of utmost importance. Injustice cannot be fought selectively, all people must stand together to fight against injustive no matter the origin.

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.