While the national ACLU doesn't believe gun rights apply to individuals (maybe "gun privileges" do), the South Dakota chapter believes they definitely do apply to resident aliens, and not just for ownership, hunting, and open carry, but also for concealed carry.
In other words, the ACLU is about as close as possible to the leftist's dream of having it both ways on rights - denying rights to US citizens while guaranteeing them to foreigners on our soil. Because of course the national ACLU doesn't just say that concealed-carry isn't a constitutional right; according to them, no level of individual gun rights is constitutionally protected, only state militias are protected. (I.e., the government can't ban itself from doing what it wants to do.) The ACLU of South Dakota is not prepared to settle for one iota less liberty for holders of green cards, even though defense against foreign invasion is one of the express purposes behind the Second Amendment.
An argument can be made that, since the Second Amendment doesn't say anything about "citizens" or "naturalized persons" but rather "the people", the rights to keep and bear do apply to everyone legally in the country. Why this necessarily includes carrying weapons concealed is never explained by the SD ACLU - an interesting question given that both the courts and most gun rights advocates accept a higher level of regulation for concealed-carry than for simple ownership, hunting, or open carry on one's own property.
As the GOA's Larry Pratt points out, the extension of these rights to immigrants is an attempt by the left to set a precedent for arming "illegals" (foreign scofflaws). The SD ACLU's move is another reason to dramatically reduce legal immigration, as well as step up deportations of foreign scofflaws. The NRA's support of the ACLU on this one, combined with their endorsement of John McCain in his senate reëlection bid, is enough to keep me from joining. I'm joining the Gun Owners of America instead.