What you are talking about is called generational sin and that has not really changed. basically it means that the next generation will be more wicked than the generation before it. Not only would they continue to practice the sins passed on to them from their fathers but they would invent new ones and pass them on to their own children That did not stop with the coming of Christ.
The Old Testament also made provision to break the curse of generational sin.
Eze 18:14 Now, lo, if he beget a son, that seeth all his father's sins which he hath done, and considereth, and doeth not such like,
Eze 18:15 That hath not eaten upon the mountains, neither hath lifted up his eyes to the idols of the house of Israel, hath not defiled his neighbour's wife,
Eze 18:16 Neither hath oppressed any, hath not withholden the pledge, neither hath spoiled by violence, but hath given his bread to the hungry, and hath covered the naked with a garment,
Eze 18:17 That hath taken off his hand from the poor, that hath not received usury nor increase, hath executed my judgments, hath walked in my statutes; he shall not die for the iniquity of his father, he shall surely live.
The generational curse is not something that God inflicts upon us but rather something that we inflict upon ourselves. The whole chapter of Ezekiel 18 pretty much deals with this issue
Moe