How can rectal prolapse cause fecal incontinence?

Not usually: A weak sphincter might increase incontinence but rectal prolapse doesn't necessarily cause incontinence other than just changing your perception of a need to pass stool if it's severe prolapse.

Sphincter can't shut: In rectal prolapse the sphincter is generally intact but because the rectum is coming out of the anus it is in a somewhat open position and although constipation is the most frequent cause of prolapse once the prolapse is full thickness any loose stool will likely escape.