Many times, literature will have more than one message. Sometimes, you have the main one, but often there will be several themes that are of equal importance. Two more themes significant to this story are love and identity.
The kinds of love shown in the story tell us that love means different things to different people. To Armand, his love for Desiree is superficial instead of a deep-seated feeling. This is shown when Armand's love for Desiree changes so quickly. Desiree's love for Armand is deeply felt to the point that she can't bear it when Armand takes his love away from her. When Armand begins to avoid her, "Desiree was miserable enough to die". Maternal love is shown by the parents. Desiree's mother wants her to bring the baby and come home. Armand's mother loved him, but she wanted to protect him from the knowledge of her African descent.
The theme of identity is also important. Desiree's childhood strips her of her true identity, but being adopted gives her a new one. A new identity is imposed on Desiree when she marries Armand. She loses the identities of her former lives and is unable to create a new one after Armand abandons her. When we learn of Armand's heritage, we learn that identity is also derived from how others see us and the qualities we possess. Armand's identity changes so quickly, showing how ridiculous it is to categorize people based on family, appearance, or any other unimportant information.
I'll be brief in addressing the story's claims:
1) Racist views are entirely constructed by humans. Armund's race is never a problem until he learns that he is part African, himself.
2) Men are selfish, conniving, and unpredictable. This comes from the complete change in Armund's behavior and treatment of Desiree once he realizes his hypocrisy. (Not sure if something about social status should be read into this as well....perhaps.)
3) Blood is thicker than water. Which is why Desiree takes the baby with her.
Hope this helps you in a pinch.
In addition, the story points out how futile and destructive racism really is. Armand desires to have a son to continue his family line, but at the end of the story he no longer has a wife or a son. If he tries to have another child, and that child appears of African decent like the first, then the secret will be revealed that Armand is really the one whose race is "cursed with the brand of slaver".