Did God change when he abolished the Law? Did God change when he issued a new covenant to Noah?
God doesn't change, but the way he deals with us does.
It also isn't true that "turn the other cheek" only refers to personal vengence. First of all, personal vengeance was already prohibited in the OT. Furthermore, when Jesus describes what burdens we have to bear in order not to resist an evildoer, he also states that "41And whosoever will force thee one mile, go with him other two." This refers to the Roman army's practice of forcing a defeated nation to carry their gear for a mile in order to humiliate them. With this Jesus teaches that even when you are persecuted severly by an army that illegally invaded you, you may not fight back!