I treasure this picture of my kids meeting the famous (other) John Henry and his driver Kathleen at the Kentucky Horse Park. Sadly John Henry has passed on. I didn't see any mention of his passing on his website- so I just wanted to mention that if you so you can be considerate to that if you do decide to contact Kathleen, I'm sure she would be very supportive and helpful.
Mules can certainly compete in CDEs, and those who have, usually are quite remarkable in their skills.
John Henry was among the first mules to compete CDE, helped get the National Rules changed for allowing them in all competitions, ridden and driven. After some time doing CDE, Kathleen decided to move on to Pleasure Driving and Showing, because JH really didn't seem to be enjoying himself and wouldn't lengthen as needed to make the times and score well in Dressage. Just not "his thing". Mules can be like that, so better to move on to more enjoyable things he had fun doing.
Mariah Carey was a smaller mule, who came thru the USA on a swing to compete in a number of CDEs in various States. She was good looking, very classy, did a GREAT job in all phases of CDE. After showing everyone how a Mule does it, and winning all the ribbons, she went on home and didn't compete visibly anymore. She and her Driver were a great pair of competitors, along with being nice folks to meet. She might have done some local things at home, but I didn't hear anything more about them after that one summer of competition.
I am sure there are other local mules playing in their areas, just not many. Mules can be quite talented, able to compete well with horses in all horse sports.
Just often takes a Special Person, rider, driver, to get that mule to show his skills, have the mule willing to do as asked. Mule folks are just different than horse folks, and many people just can't communicate well with both horses and mules. The good mules ARE GOOD, can be quite amazing to watch compete. But they have to really trust you before they will do as asked.