“Turning the other cheek” is not a passive act
Ye have heard that it hath been said, An eye for an eye, and a tooth for a tooth: But I say unto you, That ye resist not evil: but whosoever shall smite thee on thy right cheek, turn to him the other also.
Matthew 5:38-40
Walter Wink, noted theologian and activist, offers an alternative interpretation of the Sermon on the Mount, the important points of which are:
In the time of Jesus, no “public act” could be performed with one's left hand, as this was the hand reserved for “unclean acts” such as wiping one's rear end.
Using a fist on someone was strictly reserved for fights between equals.
So, if someone were to “smite thee on the right cheek” it would have to be a back-handed blow, which was reserved for underlings.
If you turn your left cheek to someone who can't use their left hand in public, then the only way they can hit you is with a fore-handed blow.
If a person hit you with a fore-handed blow, he was demonstrating that he saw you as an equal.
By turning the cheek, then, the inferior party is saying “I'm not inferior to you, I'm a human being. I refuse to be humiliated any longer. I'm your equal, I'm a child of God, I won't take it anymore.
Walter Wink — Nonviolence for the violent
As for “resist not evil”, Wink explains that a better translation would be “don't violently clash with” evil. He asserts that King James didn't want any Bible verses to seem to advocate disobedience to the “powers that be” and thus we get the admonition not to resist.
But clearly Jesus did resist evil. In the sermon on the mount, Jesus is calling on others to join in this resistance by these acts of civil disobedience.
The point has been made; the powers that be have lost their power to make people submit. And when large numbers begin behaving thus – and Jesus was already depicted as addressing a crowd – you have a social revolution on your hands.
Walter Wink — Nonviolence for the violent
Everyone is enmeshed in their lives, and we don't always have the economic or physical power to resist evil outright. But we can do it in subtle yet powerful ways. Imagine for example if you were a German mechanic during the 3rd Reich; maybe you could put small holes in the brake lines of military vehicles. Or if you were a poor but free man in the American south during slavery; you could turn your back as a slave escaped. Small acts, added together, can have large consequences.