A civil libertarian would reject the notion that a government should restrict you from a personal activity (which parenting certainly is) - because of society's majority judgment against it. They'd easily call this tyranny of the majority - whether you agree with it or not.
However, a "classic liberal" would come at this from a natural law or humanist perspective and say there is a moral reason to do / not to do such things.
There is a distinction between civil libertarians and classic liberal civil liberties.
Talk to a social worker and see whether or not you still believe that a government should still be able to step in and tell you how to treat a member of your "tribe"
I remember reading one social worker's long diatribe about why they burned out and quit. Out of several truly horrible things (black and blue children are ten a penny), the one that really stuck in my mind was the description of finding genital warts on the anus of a 7-year-old because his mother repeatedly whored him out.
"Self regulating"? Bollocks.
However, the prevalence of abuse and neglect in the foster care system - complete with cases on that order of horror - makes a very weak case for the idea that external regulation accomplishes any better.
If you had a drug that could save 50% of terminally ill patients, would you say "we have a very weak case that this drug saves lives"?
In order for your statement to make sense, the failure rate of foster care would have to approach 100%. Again, talk to an actual social worker about how they see foster care and whether or not they choose to use it. It's an opinion that will most likely come with caveats, but foster care is also a service they use frequently.
Untrue. Children end up in the foster care system for a variety of reasons, including simple loss of parents or a woman (or teenage girl) knowing she can't care for a child.
"significantly lower proportion of those kids neglected or abused"
The evidence is not as clear on this as you'd like it to be.
To correct your example, if we had a drug that caused strokes or death in a significant percentage of cases, simply saying, "Well, many of the patients we'd give it to would otherwise suffer strokes or death," would be a quick route to an FDA rejection.
Back to the point though - you could get married to 10 spouses in front of God and your friends and never tell the government about it, and I doubt they would care (unless your cohabitation violated some health code or something).
I think parents still have a legal obligation to not be negligent. There's a difference between not providing any care (while playing WOW all day) and doing your Christian Scientist damnedest for your children. A person espouses civil libertarianism not because they hate government, but because they trust people and hold others to the personal commitments they make.
Mormon polygamy: the government shouldn't be telling you who you can or can't marry.
Christian sects that disapprove of medicine: the government shouldn't be forcing you to make changes to your body.
Ritual circumcision (especially when the mohel sucks off the debris from the penis with his mouth): sounds gross to me, but the government shouldn't tell you what changes you can't make to your body, or how you provide care for a member of your tribe.
Can government intervention in these areas bring about greater human well-being? Possibly, but I think the above are relatively self-regulating. Christian sects that disapprove of medicine (Christian Scientists for example) must contend with proliferating evidence of the benefits of scientific medicine. As long as scientists have freedom of speech too I suspect their membership will continue to decline in the US.
Can government intervention in these areas bring about greater suffering? Absolutely. The US government currently intervenes in gay marriages, and recently intervened in abortions (and many in Congress would love to intervene here again!).