In this scene, the neutral Rick is confronted by the Resistance leader Laszlo (who is also the husband of the woman Rick loves). He refuses to take sides, even against the Nazis… until Laszlo seizes the day and starts a singalong battle. Watch how the bandleader looks to Rick for permission to start playing the French liberation anthem… and how Rick nods slightly. That nod is his point of no return. He has, in fact, chosen sides, and will now be an enemy of the Nazis.
(Rick is, not to be heavy-handed, a symbol of the United States before Pearl Harbor, neutrally standing by as Europe fell.)