There have been many reports on bugs like this, but none are exactly the same.
Whenever I ride an entity that is tamed and saddled, slow falling and jump boost don't work. However, if I'm currently not riding the entity the effects do work.
The tamed and saddled entities that this applies to are:
I tested this out on pigs and striders as well, but since they are not tamed the effects still work. I also tested it on a skeleton horse, but since it doesn't use a saddle (And you technically can't tame it) the effects also still work.