I think that the frequent bowel movements associated with Celiac's disease would contribute to a rectal prolapse; therefore, the more the Celiac disease is under control, the better. Any diet that is bowel-friendly is good. I tried the gluten free diet but found it didn't make any difference. By trial and error, you'll get an idea of what works for you. I keep a stenographer's pad handy and make a daily note. It helps in keeping track. On Dec. 11, I will be seeing yet another surgeon: the sigmoid prolapsed this summer, and it's taken this long to get an appoint. The Medical system in B.C. Canada is overburdened.
I just read your other posting where you say you don't have Celiac's disease but chronic consitpation. Any straining would contribute to rectal prolapse. The aim is for a regular soft stool.