Parents in his position may be thinking they can't make their adult children heterosexual or completely chaste or monogamous but their actions can affect just how promiscuous or abandoned or reckless the children become. They could be terribly wrong about that, but I don't really see people engaging the argument.
When a child of a high profile public personality “comes out,” the child pretty much has the upper hand; he can cause as much disruption as he wants, which will reflect poorly on the public figure, who has the most to lose. It is usually the path of least resistance to “go along to get along” and preserve his career. Chaney did this, as have several other politicians.
It’s really a pernicious form of extortion.