There is little to add here to the comprehensive response afforded above. However, as a subjective opinion that remains after numerous viewings, one of the most refreshing aspects of the iconic film, Casablanca--is it not curious that the name of this port denotes white house--is the cynicism of Rick and the humorous amorality of Captain Renault. That this tone is evident in a film about the war in 1941 is exceptional; most war movies were chauvinisitically supportive of the "noble cause" of war.
Rick's patriotism does not, then, seem to rise after its defeat from the nobleness of his heart. So, at best, Rick acts out of respect for the memory of his love for Ilsa. Moreover, he decides, like one of Hemingway's heroes, that he must create from the nothingness of his life in the desert of Casablanca some meaning. And, for this existential reason he acts, not from any great ideal of the nobility of the glory of the Resistance. He and Captain Renault have "the beginning of a beautiful friendship" because they both understand the reality of things and can, perhaps, find "a clean, well-lighted place" together.
I would say that you are probably always going to get a subjective analysis of any work of art. The nature of art is that it impacts individuals on different levels. The way one person reads a work of art and how another does may very well be two different extremes and it is this exploration that makes art fascinating. I would certainly say that what I offer is subjective and might be challenged by what others see. You will have to sort out these opinions for yourself as well as your own feelings about the world. I see the theme of the film as one which suggests the power of resistance and that all human beings have a moral and ethical obligation to a higher notion of the good that might remain dormant, but is one that will be heard at some point. Another way of phrasing this theme is that in the desire between duty and desire, duty will win out in the hearts and minds of all human beings. Victor Laszlo hears this calling early on, Ilsa hears it when she hears Victor is alive and leaves Rick to go to him. Rick hears it early on in his life when he supports "the losing side" in his endeavors and hears it again when he recognizes the need to give Ilsa and Victor the letters of transport. Louis hears it when he covers for Rick. The tone of the film is to express this theme or idea in operational settings. It does not demonstrate this theme in a didactic or moralizing manner. Rather, it presents situations where characters are pitted in this brutal sense of duty vs. desire and then has them choose the former, understanding its transcendent and compelling nature. The tone is one that tells a story, "a fight for love and glory and tale of do or die." It tells the story of these different characters set against a backdrop of historical events spinning the world out of control. The tone is an interesting one for while it argues that there is historical inevitability that governs human action, making human action almost moot in the face of such a force ("The problems of three little people don't amount to a hill of beans in this crazy world"). However, we understand that human action is important, is vital, and needed in this setting. The tone of the film walks this "harmonious schizophrenia" in suggesting historical causality (Recall the turning of the globe/ map in the beginning of the film and the droning of "wait, and wait, and wait) can coincide with human empowerment. When Rick says those words to Ilsa, the tone of the film proves him wrong. The problems of three little people do matter. They are vital. They are meaningful and the tone of the film explores both this reality and the one that suggests human beings are a cog in the machine of history.