One case was Levy v. Louisiana - 391 U.S. 68 (1968), about whether an illegitmate child can file a wrong death suit in behalf of his dead mother. The US Supreme Court ruled:
However that might be, we have been extremely sensitive when it comes to basic civil rights (...), and have not hesitated to strike down an invidious classification even though it had history and tradition on its side. (Brown v. Board of Education,...). ...While that may sound reasonable, should a plaintiff have to prove dependency, caring, nurturing, biology, and spirituality? No, the state defines legal relationships to simplify the law and make it unnecessary to prove those other things.
Legitimacy or illegitimacy of birth has no relation to the nature of the wrong allegedly inflicted on the mother. These children, though illegitimate, were dependent on her; she cared for them and nurtured them; they were indeed hers in the biological and in the spiritual sense; in her death, they suffered wrong in the sense that any dependent would.
The dissent said:
The Court today, for some reason which I am at a loss to understand, rules that the State must base its arbitrary definition of the plaintiff class on biological, rather than legal, relationships. Exactly how this makes the Louisiana scheme even marginally more "rational" is not clear, for neither a biological relationship nor legal acknowledgment is indicative of the love or economic dependence that may exist between two persons. ...At first glance, this case seems to be just a good civil rights decision that bastards have full rights as persons under the law. But no one ever denied civil rights to bastards. The issue was whether the state can codify family relationships. That is, can the state require registering a relationship before allowing a lawsuit based on that relationship? The court said no.
The rights at issue here stem from the existence of a family relationship, and the State has decided only that it will not recognize the family relationship unless the formalities of marriage, or of the acknowledgment of children by the parent in question, have been complied with. There is obvious Justification for this decision. If it be conceded, as I assume it is, that the State has power to provide that people who choose to live together should go through the formalities of marriage and, in default, that people who bear children should acknowledge them, it is logical to enforce these requirements by declaring that the general class of rights that are dependent upon family relationships shall be accorded only when the formalities as well as the biology of those relationships are present.
The next case, Gomez v. Perez - 409 U.S. 535 (1973), directly concerns child support:
The issue presented by this appeal is whether the laws of Texas may constitutionally grant legitimate children a judicially enforceable right to support from their natural fathers and at the same time deny that right to illegitimate children. ...The dissent said:
Under these decisions, a State may not invidiously discriminate against illegitimate children by denying them substantial benefits accorded children generally. We therefore hold that, once a State posits a judicially enforceable right on behalf of children to needed support from their natural fathers, there is no constitutionally sufficient justification for denying such an essential right to a child simply because its natural father has not married its mother. For a State to do so is "illogical and unjust." Id. at 406 U. S. 175. We recognize the lurking problems with respect to proof of paternity. Those problems are not to be lightly brushed aside, but neither can they be made into an impenetrable barrier that works to shield otherwise invidious discrimination.
With the issues so vaguely drawn and the alleged discriminations so imprecise, I would dismiss the writ of certiorari as improvidently granted.This decision was a direct blow to the ancient idea that a man marries a woman in order to take responsibility for the resulting kids, and to the advice that woman should get a ring before having kids.
The upshot of these cases is to destroy the state's ability to use its laws to discourage out-of-wedlock kids. The states are prohibited from making that distinction, and women are assured that they will get just as much child support money if they never marry.
My guess is that these court decisions did not get much attention because people foolishly thought that they were humanitarian and harmless efforts to avoid stigmatizing illegitimate kids. But the decisions really help the single moms, and encouraged a whole lot more illegitimate kids. This is another example of the law of unintended consequences.
Dalrock has more data on the rise of illegitimacy. He shows that histories of child support, such as here and here, ignore the above court decisions. An exception is this 2007 paper by Betsey Stevenson and Justin Wolfers:
Thus these changes mean that a marriage cannot be a binding union (either spouse may unilaterally divorce), cannot offer legitimacy benefits to kids (the state cannot discriminate), and cannot provide for support of the kids (state child support obligations are independent of any marriage contract).
Supreme Court rulings in the 1960s and 1970s also changed the nature of family relationships by eliminating many of the legal distinctions stemming from the marital status of a child’s parents. ...
Currently all but five states have some form of unilateral divorce and two-thirds allow unrestricted unilateral divorce.
These legal changes fundamentally alter the basis of the marriage contract. They remove the ability to make intertemporal contracts within marriage — one spouse cannot promise not to leave his or her spouse in the future. They shift the right to divorce (and hence bargaining power) from the party most interested in preserving the marriage to the person who most wants out of the marriage.
Libertarians sometimes talk about letting people have the freedom to write their own marriage contracts. The concept of people voluntarily taking on the rights and responsibilities of marriage seems to great to me. But it is a legal impossibility unless a whole list of laws and court decisions are reversed, and I never hear about any libertarians or LGBTQIA advocates pushing for those reversals.