Many traditional songs started as popular songs written for money. Some were in musical shows, theatrical presentations or played in band concerts. Today, licensing organizations are jealously guarding their "intellectual property" and even today music
played at farmer's markets for musician's tips are being targeted by ASCAP in California, as well as Girl Scout Campfires.

OTOH Dylan and Guthrie used many tunes taken from tradition for their lyrics. Some have called it piracy but I think of it as being the folk tradition.

Sometimes the traditional singer overlaps with the professional performer who makes money at it. Uncle Dave Macon would be an example. A.P. Carter rewrote many traditional tunes or just claimed them for money. Jimmie Rodgers, the Carter Family,
and many of the tradition-based early country music performers did the same thing.

You can take a traditional tune, copyright it, usually with a different set of lyrics ie:
"The World's on Fire" to "This Land Is Your Land" but if someone decides to write those melodies with a different set of lyrics, those lyrics should be able to hold up in a court suit as original. Woody's tunes were copyrighted by Ludlow Music, BMI in New York City by Howie Richmond. Woody claimed ownership (rather did Ludlow Music) of a tradtional "Buffalo Skinners" setting the traditional lyrics to another tune other than found in Carl Sandburg's "American Songbag" from the 20's. Dylan made a lot of money appropriating traditional tunes. Stealing tunes

Peggy should never had been shut out by music moguls. If she had lots of money,
she could have fought it in court.

The stealing of tunes and ideas is an important part of the folk process. OTOH if someone decided to write a lyric based on Jerome Kern's "All The Things You Are",
this becomes problematic because the tune has entirely originated with the composer.
However, a parody or bowdlerization of the tune with new lyrics could fit in with the notion of the folk process.

There has to be a rewritten copyright law to allow for changes to be made in existing
songs that are claimed by lyricists and composers. Adaptations are copyrightable
but would you call "Masters of War" or "Don't Think Twice" an adaptation? They both are based on antecedent melodies. Stealing a lyric is not OK but stealing a tune is?

What about stealing story-themes?

It's very complex because there is sometimes a lot of money involved. There is little consistency in copyright law however.

Folk singers who change things need a good lawyer today.