A little more info will help. Not knowing if you are the original owners-----If you are, have you ever cleaned the roof? That might be one place to start. A good scrubbing with either spic & span, or solvit might get rid of that white residue. If the rig has sat out in the hot sun all of it's life, might be a reason for it. If you are not the first owner, then you don't know what was used on the roof before.
2008 Cruiser CF26RK
2013 Ford Eco-Boost
Heavy duty payload - Max tow
I have seen this a lot with my PP. A good washing (I use comet with a brush and a good rinse) and I do use a rubber roof treatment after it has dried. If you do this a couple times a year it seems to keep it in check. My roof also has gray spots not all nice and white but I think it is the sun and it has been that way since new. If you can keep the roof in good shape the runoff will not stain the side of the trailer.
Hope this helps answer your question
George and Debi
2006 F250 PSD, 2005 PF30CK
I am quite agree with the Old farmer. can you used some plastic paper which is give support from the rain water.. Or don't know much more about the rubber roof treatment. but try it one time at lest you will get a experiences.