The ironic thing about all this is that Conservatives have traditionally championed causes that can only be described as collective parenting- legislating morality by censoring things for all children under a certain age, campaigns and PSAs about negative music, movies, videogames, religious propaganda, waging "culture wars," complaining that secularization means "no holidays for the children," etc. One of the most common Conservative arguments against the mainstreaming of homosexuality and gay marriage is that "our kids shouldn't have to see that," as if they can speak for all parents.
Furthermore, old-fashioned American and most old world immigrant values encourage exactly this attitude- people's neighbors did and still do tell them about their own kids, discipline them, etc. But of course, this ad isn't referring to any of the above.
Hyping up this ad and twisting its message into some kind of hivemind propaganda or anti-individualist screed is ridiculous, though. The message should be agreeable to most. Hyperindividualist Margaret Thatcher-style "there is no society, only individuals and their families" attitudes are fundamentally wrong and negative. Some robust notion of community is important, and a general investment in the future, for the sake of each individual, necessarily involves including that notion of community, and therefore children in general, in it. Individualism quite literally ignores itself when it forgets community.
I want to see children in general succeed, not just the one who are related to me, and part of what her idea entails is creating a proper culture of parenthood in society that all families, especially those in the Black community, could benefit from- it's not actually at odds with Conservatism at all, unless you twist it far out of proportion.
No, that's only part of the picture. The other part, which itself contributes to that breakdown, is neoliberal economic policy that's based on a hyperindividualist notion of the citizen and an ignorance and demonization of any and all forms of collectivity that aren't "the market" (as if that's even really a collective endeavor in free market theory.) It destroyed everything that was good about the social programs and services in Black neighborhoods. That nonsense is precisely the problem.