Rick, Bogart's character, was a lefty who fought in Spain.
One of the screen writers went on to write Mission to Moscow and was blacklisted.
Casablanca and the Marx Brothers had a huge following with 60s college kids, often radicals.
Maybe it was a matter of a generation picking something from their parents' generation and taking it up.
Something similar happened with Sha-Na-Na and American Grafitti in the 1970s and with the Rat Pack back in the 1990s.
When you grow older the next generation isn't going get enthusiastic about something from their grandparents' day.
You should see Everybody Comes to Rick’s (the actual basis for Casablanca), or at the very least read its script. It’s better, and I can definitely confirm that him running guns for Ethiopia or his involvement in the Spanish Civil War was NEVER in the play at all and was exclusive to the film. In the play’s equivalent to that scene, Rinaldo simply mentioned Rick’s full name, Richard Blaine, his nationality, his age (which was given discreetly), that he was formerly a successful attorney in Paris, was formerly married to the daughter of Alexander Kirby, had two children with her, had left Paris in 1937 for undisclosed reasons (whatever caused him to leave was apparently serious enough that Rick tensed up at Rinaldo even mentioning the event he left Paris in passing, causing him to wisely skip over that), and that he ended up divorcing his wife at Reno, with the latter keeping custody of his children (Rinaldo’s “shall I go on” after that suggests there’s more to it that was unrevealed). Most likely, the Spain bit and Ethiopia was added in by that screen writer you alluded to, Howard Koch, as a subtle attempt at promoting solidarity with the Communists.
If you don’t believe me, you can see for yourself: http://www.pages.drexel.edu/~ina22/splaylib/Screenplay-Everybody_Comes_to_Rick’s.pdf I will warn you that Page I-17 is unfortunately largely obscured.
It was purely anti-Nazi, with Communism not even being a factor into it (and good thing too, because I have respect for those who are both anti-Nazi and anti-Communist, and do not like people who condemn Nazism yet promote Communism, or for that matter people who condemn Communism yet promote Nazism.).
I do wonder what you mean by the Marx Brothers having a huge following with 60s college radicals, though. Other than their sharing the same last name as Karl Marx, I fail to see what ties them in to student radicals. They’re just a comedy group, and don’t seem to have any ties to socialism or communism or anything like that (at most, they might have a passing tie to the New Deal).