In the story "A Good Man is Hard to Find," what qualities about the family are meant to be taken seriously?

O'Connor would want us to care about the family's souls.  She would want us to ask, "Why does this family, if 'saved' by the blood of Jesus, try to save themselves from death?"  Her implicit answer seems to be that most people ironically worry about their souls most when they are about to lose them.  If this is the case, she seems to be saying that we should live every day as if we had a gun to our head.  She certainly did: she was diagnosed with a fatal case of lupus, which was a death sentence that looms over all of her writing.

"A Good Man is Hard to Find" (1955) tells the story of a family en route from Tennessee to Florida for vacation. Through a series of the mishaps by the grandmother and her cat, the family car wrecks near some woods in Florida. Two witnesses from a following car stop to aid the family, all of whom are relatively unscathed. The grandmother identifies one of the witnesses as The Misfit, a mass murderer on the loose.

Her admission is a death sentence for the family. The Misfit's accomplice takes the family into the woods and shoots them. The grandmother tries to save herself by pleading to the Misfit, "You've got good blood! I know you wouldn't shoot a lady! I know you come from nice people! Pray! Jesus, you ought not to shoot a lady. I'll give you all the money I've got!"

The Misfit responds:

Jesus was the only One that ever raised the dead and He shouldn't have done it. He shown everything off balance. If He did what He said, then it's nothing for you to do but thow away everything and follow Him, and if He didn't, then it's nothing for you to do but enjoy the few minutes you got left the best way you can--by killing somebody or burning down his house or doing some other meanness to him. No pleasure but meanness.

Just before it is her turn to be shot, the grandmother says:

Why you're one of my babies. You're one of my own children!" She touches the Misfit on the shoulder, and he springs back "as if a snake had bitten him and [shoots] her three times through the chest.

The Misfit tells his accomplice to throw the grandmother into the woods with the others, adding: "She would have bee a good woman if it had been somebody there to shoot her every minute of her life."