The "cops and legislators"/agitators line is in Rise Up Singing....and I wouldn't trust it as authentic. As you know, I work for Peter Blood and Annie Patterson as a lyrics editor, and I have had many arguments with Peter Blood about revisionisms like this. I wasn't around for the production of Rise Up Singing, but I won most of my battles on Rise Again and a subsequent Pete Seeger songbook.
Woody changed his words all the time, so I guess the "agitators" line could be his - but I doubt it. I listened to four different Woody recordings of the song, and all of them had more-or-less this same chorus:
CHORUS: Jesus was a man, a carpenter by hand His followers true and brave One dirty little coward called Judas Iscariot Has laid Jesus Christ in His Grave
The Guthrie Family has done a pretty good job on compiling Woody's lyrics, but they usually have only one version of a song. Here's the version of "Jesus Christ" that they have: https://woodyguthrie.org/Lyrics/Jesus_Christ.htm
I used to think that the lyrics in Sing Out! were accurate, but I found out differently when I worked on Rise Again. The magazine had a lot of sloppy transcriptions. When I did the lyrics transcriptions for Rise Again, I tried to find two printed sources and two recorded sources for each song....and even that wasn't infallible.