The musicians and actors noticed that Heinz-Christian Strache was among the audience at the Domplatz on Tuesday afternoon, sitting with his FPÖ colleague Johann Gudenus in the fourth row.
They then decided on an impromptu performance of the well-known socialist song The Internationale, as a form of protest against the FPÖ's politics.
"This was an unplanned, spontaneous action, and we stand by it," drummer and percussionist Robert Kainar said, who leads the ensemble013 orchestra performing in Everyman.
A dinner party scene in the play leaves some room for improvisation, which is when the musicians decided to ad lib. Kainar told the Salzburger Nachrichten newspaper that he lamented the fact that well-known Austrian musicians and artists often fail to take a position on political issues.
The musicians' protest was apparently lost on the two politicians. Strache told media that he hadn't noticed the musical interlude and Gudenus said the ensemble was entitled to its artistic freedom.
So far the Salzburg Festival direction has not issued any statement on the incident.