My Halflinger mule (my Halflinger mare and Mammoth jack) is 25 now, and the biggest obstacle I’ve had to overcome with him is his fear isssues. Couple that with the donkey genes that make him instinctively brace against pressure, his downhill conformation and ability to resist pressure, and he’s been a 25 year learning experience.
He was started in harness as a 3 year old, which, with 20/20 hindsight was a mistake because it was way too much for him mentally (he was scared silly the whole time).
Then, when he was about four I started clicker training him because I wasn’t getting far with pressure and release (due to my unreasonable expectations from my previous experiences with horses and his seemingly off the charts fear issues).
Clicker training with him was the proverbial “voyage of discovery”, and I’m still working on that 20 years later. I did a lot of dressage with him because that’s what I do, and am happy to say that he’s now calm, straight, and has a good relationship with the bit (doesn’t wear a noseband and doesn’t gape his mouth or chomp the bit).
I free shaped a lot of what he knows because I wanted to learn how to do that, and he needed that kind of time, but I do feel that trying to go up the levels on him would been a mistake simply because he’s not built for it. So I stuck with trail riding and perfecting lower level work instead of pushing for more advanced work.
I took him to one small local schooling show, training level, and he didn’t panic and stayed in the arena by himself, so it went pretty well. He can blow through a snaffle like it isn’t even there, so he did okay, and if I didn’t already have a horse who is much better built for dressage I probably would have done more of it with my mule.
I think the reason mules may have a rep for being less supple is because if they have a reason to resist they’re able to really, really resist, even though they’re perfectly capable of flexing and bending when they don’t have any serious reservations about doing it.
You can see both in this clip. When he has to look he has to look, and no amount of pressure is going to make him look away when he really needs to look. But when he’s feeling safe enough he’s willing and able to go along with whatever I want to do.
Ten years ago, back when I was still in my 60’s and still interested in going to shows. 
https://youtu.be/3_QLuZGIq9M