Federal law doesn't bar permanent resident noncitizens from getting guns, and neither does Washington State law. But Washington law requires that noncitizens get a special alien firearm license, and the state Department of Licensing is refusing to issue such licenses:

We are unable to issue alien firearms licenses at this time.

The Federal Bureau of Investigation (FBI) has told law enforcement agencies it is against federal law to use federal databases for background checks if they share the results with a non-criminal justice agency such as the Department of Licensing. As a result:
* Law enforcement agencies cannot perform the background checks required by state law for issuing an alien firearms licenses.
* We cannot complete the application process or issue alien firearms licenses.

The NRA, the Second Amendment Foundation, and several permanent residents who live in Washington are now suing, claiming this violates the Second Amendment (which they argue is incorporated against the states via the Fourteenth Amendment) as well as the Equal Protection Clause and 42 U.S.C. § 1981. For more on the general legal theories involved, see this post of mine from three months ago. For more on the litigation, see this Seattle Post-Intelligencer article. Note that the Washington Constitution's right to bear arms is of no help to noncitizens, because — unlike some other state constitutions (e.g., Nebraska's) — the Washington Constitution secures the right only to each "individual citizen."

By the way, here's the 42 U.S.C. § 1981 theory, which my earlier post didn't discuss:

1. This statute — enacted shortly after the Civil War — provides (emphasis added), "All persons within the jurisdiction of the United States shall have the same right in every State and Territory to make and enforce contracts, to sue, be parties, give evidence, and to the full and equal benefit of all laws and proceedings for the security of persons and property as is enjoyed by white citizens, and shall be subject to like punishment, pains, penalties, taxes, licenses, and exactions of every kind, and to no other."

2. This doesn't just bar race discrimination, but also discrimination against noncitizens (as to the subjects involved).

3. The state constitutional provision securing a right to bear arms, and state laws related to concealed carry licenses, are "laws ... for the security of persons and property."

4. Therefore, discrimination against "lawfully admitted resident aliens" violates § 1981.

Note: Though the logic of this statutory argument might extend beyond lawfully admitted resident aliens, federal gun statutes generally bar gun possession by illegal aliens and by most aliens who have nonimmigrant visas. These statutes likely implicitly limit § 1981 as to those kinds of aliens. And even if § 1981 continues to preempt state laws limiting ownership by such non-lawful-immigrant noncitizens, federal law would make such ownership illegal and thus make the state law question largely moot.

Thanks to Venkat Balasubramani for the pointer.