Rutherford & Co were prosecuted under the Espionage Act. The specific charge was interfering with the ability of the United States to raise an army during wartime.
At issue were a few pages from the book, The Finished Mystery
Another tidbit that the Society doesn't like to publish, which can been gleaned from the transcripts, is that Rutherford and the Society actually cowered, and removed the offending pages from already-published copies of the book. Hardly the shining example of boldly proclaiming the truth in the face of persecution from Satan's system.