"Musicians ask Republican candidates to stop playing their songs"

[True Federalist (진정한 연방 주의자)]

I'm surprised any campaign would be playing songs without permission from the artists.

They tend to think copyright laws apply only on the internet.

More likely the artists are no longer the rights holders.  Unlike Europe, U.S. copyright law does not generally recognize the concept of an inalienable moral right to determine how their songs are used. That makes using a song the artist doesn't want used by a political campaign a PR problem, not a copyright problem.