To be able to properly answer this question, let's first review the way that Armand behaves in the short story "Desiree's Baby" by Kate Chopin. Desiree is an orphan left outside the gate of the plantation of Monsieur and Madame Valmonde. The Valmondes adopt and raise her. When Desiree is standing beside the gate as a young woman, Armand rides by and falls in love with her. He marries Desiree and takes her back to his ancestral plantation. Soon, they have a baby boy.
Tension arises after the boy is a few months old and it is obvious that he is dark-skinned and not purely white. Armand accuses Desiree of not being white; he rejects her and the child. In despair, Desiree takes the baby, wanders off into the bayou, and presumably dies. At the end of the story, we learn that Armand's mother was black, and the baby's skin tone is due to his ancestry, not Desiree's.
The behavior in question is Armand's rejection of Desiree and the baby, and cover-up of his own ancestry. At that time in history, black people were bought and sold as slaves. Very few of them were free citizens. To be identified as having African heritage instead of being white meant a profound change of status; as a result, many people, like Armand, would do anything to avoid this stigma and racism.
The social situation today is certainly not the same as it was during the era of history in which the story takes place. African Americans are citizens who have the freedom to marry whoever they want and do whatever they want (even if there are still many structural barriers in American society). There are many examples of successful mixed racial marriages in our society. However, there is still a lot of prejudice against African Americans in this modern era. Statistically, black Americans have lower incomes than white Americans, and their poverty rate is more than double that of white people.
It is possible that some people of mixed racial heritage, even in our modern society, might try to cover up their black ancestry like Armand does in the story. Some might think that they would have more advantages if people think they are white. It's also possible that some people would be hateful enough to reject their loved ones, even nowadays, if they found out that they might have a mixed-racial background. However, it is much less likely that it would happen today than back in the era of the story, which was the time when slavery cast a horrible pall on all aspects of American society.