Even before we know that Mae is immortal (which, let's face it, is kind of a big deal), we can tell what kind of person she is. Check out this first conversation we hear her have with her husband:
Mae sat there frowning, a great potato of a woman with a round, sensible face and calm brown eyes. "It's no use having that dream," she said. "Nothing's going to change."
"You tell me that every day," said Tuck, turning away from her onto his side. "Anyways, I can't help what I dream."
"Maybe not," said Mae. "But, all the same, you should've got used to things by now." (2.5-7)
Sure, we have no idea what they're talking about, but it's pretty clear that Mae isn't a dreamer. She's down-to-earth and practical. They are what they are. That's it. The end.
Why is she able to be this way? Well, Mae has definitely lost a lot of things by becoming immortal, but she still seems to have the things that really matter to her: her husband, her sons, and her music box. She doesn't mind moving every so often or keeping to herself. She has her family, and that's what matters.
We might be a little shocked when we see Mae come at Yellow Suit Guy with a shotgun. The narrator doesn't take us inside the thought process that led Mae to that point. Instead, we just watch, along with Winnie and the other characters, as Mae acts. Why does she do it? Well, she answers that question pretty clearly.
But Mae's face was dark red. "Not Winnie!" she said between clenched teeth. "You ain't going to do a thing like that to Winnie. And you ain't going to give out the secret." Her strong arms swung the shotgun around her head, like a wheel. The man in the yellow suit jerked away, but it was too late. With a dull cracking sound, the stock of the shotgun smashed into the back of his skull. He dropped like a tree, his face surprised, his eyes wide open. (19.37)
Mae loves Winnie and her family too much to risk letting Yellow Suit Guy have his way. But it's up to you to decide: does that make it okay?