Nordyke v. King. For those who count such things, the unanimous panel consists of a Reagan appointee (Judge O'Scannlain, who wrote), a Carter appointee (Judge Alarcon), and a Clinton appointee (Judge Gould).

The panel avoids the late 19th-century cases United States v. Cruikshank (1876) and Presser v. Illinois (1886) by reading them as simply foreclosing the direct application of the Second Amendment to the states, or the application of the Second Amendment to the states via the Privileges or Immunities Clause. The panel instead follows the Supreme Court's "selective incorporation" cases under the Due Process Clause, and concludes that the right to bear arms "ranks as fundamental, meaning 'necessary to an Anglo-American regime of ordered liberty.'" And in footnote 16 it points out that

Because, as Heller itself points out, 128 S. Ct. at 2813 n.23, Cruikshank and Presser did not discuss selective incorporation through the Due Process Clause, there is no Supreme Court precedent directly on point that bars us from heeding Heller's suggestions. Cf. Rodriguez de Quijas v. Shearson/Am. Express, Inc., 490 U.S. 477, 484 (1989) ("If a precedent of this Court has direct application in a case, yet appears to rest on reasons rejected in some other line of decisions, the Court of Appeals should follow the case which directly controls ...."). But see Maloney v. Cuomo, 554 F.3d 56, 58-59 (2d Cir. 2009) (concluding that Presser forecloses application of the Second Amendment to the states).

(I should note that many scholars view Due Process Clause incorporation as historically unfounded, but take the view that the Privileges or Immunities Clause was originally understood as incorporating nearly all of the Bill of Rights against the states; but that is not the view the Supreme Court has taken.)

This sort of "fundamentalness" reasoning in naturally mushy — as it has been throughout the Court's selective incorporation cases — but here's roughly how the panel goes through it: (1) It points to evidence that the right was seen as very important by the Framers, and concludes, "This brief survey of our history reveals a right indeed 'deeply rooted in this Nation's history and tradition.' Moreover, whereas the Supreme Court has previously incorporated rights the colonists fought for, we have here both a right they fought for and the right that allowed them to fight."

(2) It points to continued support for the right from the Framing on, noting among other things that 44 state constitutions contain a right-to-bear-arms provision.

(3) It particularly points to the support of the right, including its self-defense component, around the time the Fourteenth Amendment was ratified.

Note that the better articulation of the test the panel actually applied was probably whether the right is "deeply rooted in this Nation's history and tradition" (citing Glucksberg), not whether it's "necessary to an Anglo-American regime of ordered liberty." Among other things, the Anglo- half of "Anglo-American" abandoned the right decades ago, and it's pretty clear that many of the rights that have indeed been incorporated (such as, for instance, the privilege against self-incrimination) aren't strictly necessary to our regime of ordered liberty. But that criticism would equally apply to many of the Court's selective incorporation cases, which probably also followed the "deeply rooted" test even if they didn't articulate their reasoning that way.

The panel's reasoning begins by pointing to the Framing Era sources

Thanks to Alice Marie Beard for the tip. Will blog more as soon as I can carefully read the opinion.