Independent voters in South Dakota are already permitted to vote in Democratic and Libertarian primaries. That is because those two parties want independents to vote in their primaries. On February 13, a bill to allow independents to vote in the Republican and Constitution Party primaries was defeated on the House floor. HB 1305 had a Republican sponsor, Representative Drew Dennert, but most Republican House members voted against it. See this story. Thanks to Shawn Griffiths for the link.