Whatever permits being publicly funded by the state is deemed a public good by the polity that funds it.
Nothing deemed to be a private good can also be deemed to be a public good by the same polity.
Therefore, nothing which permits being publicly funded by the state is a private good
Whatever is deemed constitutionally protected under the justification of privacy is a private good. Since private and public are mutually exclusive categories, no such goods are public goods.
Public funding for abortion is required by law in multiple U. S. jurisdictions, and hence would be deemed a public good by those same jurisdictions.
By the same criterion, it cannot constitute a private good in contradistinction to a public one, and thus cannot be legally protected under grounds of privacy.
But the grounds on which abortion is legally protected are exactly those of privacy.
Thus, if abortion is constitutionally protected on the grounds of its being a private good, then it is not permissible to publicly fund it. Likewise, if abortion is publicly funded, and hence treated as a public good, it is not constitutionally protected.
Therefore, abortion may be publicly funded in U. S. jurisdictions if and only if it is not constitutionally protected.