I am not too sure why the red hunting hat would protect Phoebe. Unless I am mistaken, the text makes no reference to the way in which Phoebe is "protected" by the red hunting hat. In a sense, the importance of the hat is not related to Phoebe, but in the way that it is given to her by Holden and what this act represents. Let us remember that throughout the novel the red hunting hat seems to be a symbol of Holden's desire to be different and his uniqueness. It is clearly odd and this indicates the way in which Holden wishes to be separated from everyone else. Note what we are told about the hat in Chapter 3 when Holden is talking to Ackley:
He took another look at my hat . . . “Up home we wear a hat like that to shoot deer in, for Chrissake,” he said. “That’s a deer shooting hat.”
“Like hell it is.” I took it off and looked at it. I sort of closed one eye, like I was taking aim at it. “This is a people shooting hat,” I said. “I shoot people in this hat.”
Note the way that Holden's desire to be unique and isolated is linked to his alienation to the world. The reference to "people shooting" indicates the violence that he feels towards the "phony" people he is with, and of course his cynicism and language does allow him to "shoot" people metaphorically. Yet at the same time the way that throughout the novel Holden is self-conscious about his hat, telling us when he is wearing it, points towards the central conflict of the book as Holden struggles with his desire and powerful need for isolation and his equal need for companionship. When he gives the hat to Phoebe, we perhaps see the beginning of the end of this conflict, as his act of giving it to his beloved sister indicates the triumph of his recognition that he needs love and companionship.
Thus the hat, from my perspective, doesn't seem to be about Phoebe much at all. If it protects her, it is only because by being given it she is not going to lose her brother, as it represents his recognition that companionship and connections are important.