Can liberal musicians stop Republicans from using their songs?

[Commentary] Despite the fact politicians usually stop playing songs when asked, songwriters could fight it if they really wanted to. According to the American Society of Composers (ASCAP) guidelines on using music in political campaigns, if campaigns obtain a public performance license from them or other performing rights organizations like Broadcast Music, Inc (BMI), they're in compliance with copyright law, which is why campaigns always first respond to statements from angry musicians by saying they were following the rules. But being in compliance with copyright rules doesn't mean musicians can't complain and even take legal action -- which is why the ASCAP advises campaigns get permission from artists' management and songwriters as well, to avoid all this.

Per the ASCAP, musicians could seek recourse through their right to publicity (which public figures have for their image in some states), false endorsement (an argument that their work is being used to incorrectly imply support for something) or the Lanham Act (dealing with unauthorized use of a trademark leading to confusion). So there are legal grounds for them to fight the song's use. But there's not much precedent for that happening, because campaigns generally give in to musician's demands so quickly.