What oomis says is what I’ve heard that a relative’s co-worker said, as to why she was looking to marry a Jew. Not that she showed much Ahavas Yisroel, though.
The first generation that strayed remembers the atmosphere in the home during their upbringing. That gives them a strong feeling of belonging to that people. In rome instances, they can impart that feeling to their children. Being that the feeling is so strong, it is tangible enough to pass down. It goes without saying, that there is a limit how long this can carry on. If I touch a towel wet from hand drying, I can’t make something else visibly wet enough.