I wanted to see for myself what dialogue differences there were if I did Riju's story third and Sidon's last. As you can see, there are some differences in what the two say, as well as what Purah and Buliara say at Lookout Landing immediately after finishing Riju's events. (and for the record, there are no changes at Lookout Landing after doing everything out of order; the game still assumes you went to Rito Village, Goron City, Zora's Domain and Gerudo town in that order.)
Start: Debrief with Riju
2:00: meeting with Purah and Buliara at Lookout Landing
2:54: Debrief with the Zoras