Racism is a big theme in Supergirl. The discrimination of aliens is a pretty big part of this show, and there’s even a mayor who is publicly anti-alien. This is very obviously a metaphor for racism. Illegal immigrants are also called aliens, so it most likely includes that aspect, too
Feminism is probably the biggest theme in Supergirl. After all, the main character, Kara Danvers, works for Cat Grant, a powerful woman with her own business. Kara is a female superhero. One of the first important interactions you see between Kara and Cat is a discussion over Supergirl’s name, which Cat chose. Kara says that she feels “girl” isn’t powerful enough and she thinks Supergirl deserves a stronger name, maybe Superwoman. Cat responds by saying that if Kara doesn’t think “girl” is strong enough, then isn’t she the one at fault?
The Holocaust really isn’t a big theme in Supergirl, but it’s important. The Green Martians were killed off by the White Martians, and J’onn J’onzz, the last of his kind, says that they were put in camps and killed off. This obviously mirrors the Holocaust where Hitler and the Nazis put Jews in concentration camps and conducted a mass genocide of their race.
Supergirl covers many controversies and I love it. This show just keeps getting better and better.