Hi Brokebacklove4ever, that 's a good question! I'm checking to see if the paper bag appears in the story too... No, it's not in the intro or in the ending either. That means the paper bags were Ang Lee's idea, a very Eastern idea, too, because any kind of container can be thought of as symbolic of the soul in Taoist religions. In fact, during the hippie era, one's passions were referred to as their "bag" as in, "That's just not my bag". It seems very awkward today in the era of the elevator speech!
There are many containers depicted in the movie, but the paper bag is one of the most poignant. It is humble and self-effacing as in the idea of the "bag lady" or "putting a bag over your head". Then, too, there's the connotation of the plain paper bag that disguises all manner of personal items. I've heard that sex toys are delivered in a "plain paper bag" although today I'm sure they're delivered in a FedEx box. Especially at the end, Ennis received the comforting anonymity of the shirts lovingly wrapped in a plain paper bag by Mrs. Twist, who understood. There's the aspect of humility and poverty. Jesus was born in a manger, and Ennis appears as a hitchhiker with all his belongings in a plain paper bag.