The meaning of "turning the other cheek" is that we should endeavor not to react in a vengeful manner when we perceive that we have been wrongly treated by others.
All the actions that proceed from us must be borne out of love instead of an evil intent which includes taking revenge by taking some actions meant to harm the other person who has perpetrated a wrong against us.
In addition, it also means that we must forgive those who offend us. That is the way we ourselves can be free. If we do not forgive those who trespass against us our own sins too cannot be forgiven! We should always remember a portion of the Lord’s Prayer that says: forgive us our trespasses as we forgive those who trespass against us. If we forgive others, we will not intentionally harm them in retaliation. Acting in retaliation only heaps up a burden of guilt on us regardless of the temporary satisfaction that the vengeful act may bring.
However, the foregoing does not mean that we should encourage others to treat us shabbily. That will be promoting evil and this is not the meaning of Christ’s Teaching. We should be fearless and face others with dignity and firmness. We should demand the same respect we voluntarily give to others and seek to be treated fairly but we should not commit a sin in that process.