I don't think trying to make someone stop being rigid is going to work; it will just make it a lot worse because the person will probably panic, especially a child. Instead find ways to work with the rigidity and just help him to relax and feel in control, which will help him to be more flexible. If someone is being really rigid at a given moment though, I would think it would be because he's really stressed out and can't handle a change, and it's better to just give in for the moment unless that would be somehow harmful or impossible.
So for example, one time a friend of mine was at my house and using a towel to wipe the kitchen counters, and I freaked out because I don't use that particular towel to wipe the counters. I told him to stop it and he said, "What's the big deal? Why does it matter? You're obsessive and overreacting, etc ..." I nearly had a meltdown. It made me feel like I had no control and everything was going to get messed up. It would have been better if he had just said, "Ok, what do you use to wipe the counters?"
I also need at least several days of mental preparation before doing anything that is not part of my daily routine, even if it's something I think is fun. Preparation time helps a lot.