I think it depends a lot on the manner of engagement and the area of life. Most pop stars don't just sell music. They sell themselves as personalities, as icons. This is often true about politicians as well. Much less so for authors and software developers, though; there, what they're offering is generally the work, not themselves.
I think keeping family out of politics is not so much about keeping one area of the public figure's life private as allowing the family members to keep their own lives private. Maybe that line is blurring, but I'm not sure the public is entirely to blame. Politicians often use families as props and even shields, as when the wife literally stands by a philandering politician in the apology press conference. And the Trump administration has actively involved the whole family in governing. So I'm not sure I'd lay changes here at the feet of social media.
I think keeping family out of politics is not so much about keeping one area of the public figure's life private as allowing the family members to keep their own lives private. Maybe that line is blurring, but I'm not sure the public is entirely to blame. Politicians often use families as props and even shields, as when the wife literally stands by a philandering politician in the apology press conference. And the Trump administration has actively involved the whole family in governing. So I'm not sure I'd lay changes here at the feet of social media.