A mixed breed rabbit will be a "pet shop" bred animal, so will not have any animal in its recent history chosen based on health and genetic screening. So you can have perfectly healthy mixed breed rabbits, and absolute health car crashes of mixed breed rabbits. Luck of the draw.
Purebred doesn't equal healthy though, have seen so many rabbits who have come from breeders end up in rescue and be an absolute mess. I'm sure there are breeders out there who carefully screen for health problems, but breeds with short skulls and lopped ears especially, tend to be prone to being a mess. Like poor little Netherland Dwarf, Gabriel, who came from a breeder to Rabbit Residence who had BRC rung rabbits. When he arrived he was in stasis and had horrific teeth and abscesses in his respiratory system and thorax, sadly he passed away after being at the rescue for a year a few weeks ago, he'd been in at the vets and had to have 5 molar teeth removed, he didn't recover well unfortunately and passed away. Poor little guy.