As one who is a firm believer that there are no biological basis to support crossdressing when seen as a behavior, my vote was “no”.
And before the nice ladies with torches and pitchforks arrive, I know that crossdressing can be a behavior related to other issues, like hormone imbalances, in utero feminization, etc.
By itself, it is, in my opinion, more likely to be originated by nurturing instead. A family where there are several CDs may share different educational/formative threads which may be less likely to discourage activities like crossdressing, to basically encouraging it.
A matriarcal family where being a female is celebrated would be a good example.
Other than that, a simplistic example would be a family where both parents attended the same college. They will cheer for the same teams, they would encorage kids to attend that same school, etc.
Or even closer to your example… Lt. Dan in “Forrest Gump”. His grand grand dad was a soldier, his grand dad was a soldier. His dad was a soldier. He was a soldier. Was that due to s biological “predisposition”? Unlikely.