There really isn't any cultural considerations for what to wear to this part Jordan. It's a desert with barely anyone around. Just pack for the temperature
There's a pretty big day/night temperature difference due to the desert
I went in May I wore shorts and t-shirt and it was still very hot during the day. But they were rather perfect at night
If you go in the fall, winter and spring (October-April), bring a sweater, jacket and trouser with you for the night time as it gets to European spring/fall temperatures
I found this handy temperature chart for Wadi Rum while researching my trip. Source