Rubber is fine, I prefer using metal though because Rubber can get chewed up as does Leather. Leather just downright scares me, not sure why people feel the need to use it...There's a reason we use it on breakaway straps, because it breaks away. Most people won't know how to maintain it, and even thick leather can have its issues if the horse is chomping on it.
If your horse likes the mullen mouth rubber, then by all means, ride him in it!
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.