Sin is not transferable. Some people argue that certain disorders which run in families are examples to demonstrate that the sins committed by an ancestor have taken the form of the disease and is running in the lineage. It should be understood that if an individual is born in a family, it means that the individual has committed such karma in his/her past lives to take birth in this family.
There is another mechanism by which sins spread. It is common knowledge that if we stay with a person for long time we tend to imbibe the qualities of that person. This fact has acceptance both in scriptures and in modern psychology. We tend to cultivate the tendencies of those we adore or admire. Similarly merits and sins are passed on. Passing on does not mean that sins leave others and run to us. While the sins of those we admire remain with them, we tend to cultivate such habits over a period of time. In this way it is possible that the sins of parents pass on to children.
Even here, it is your past karma that exposes you to such environment. Because you had to commit sins, you had to take birth in that particular family. It is not proper to think that you are suffering for the sins of your parents.
(Q&A Bhaktimala Jan 1998)