The Ukrainian military has labored, for years, to root out far-right extremists in its ranks. The latest clash between the extremists and the defense ministry in Kyiv couldn’t have come at a worse time—or in a worse place. After weeks of drama, the defense ministry redeployed and shook up the staffing within the army’s 67th Mechanized Brigade this weekend. The brigade was holding the most vulnerable district in the most vulnerable city in eastern Ukraine’s Donetsk Oblast: the canal district of Chasiv Yar. Now the 67th Brigade—what’s left of it—has redeployed to the Ukrainian rear, and a brigade of Ukrainian...