All high-impact workouts put strain on your feet and ankles, but Crossfit’s mix of weights, jumps, and cardio means you’re rapidly switching between activities which put very different types of pressure on your feet.
Crossfit has a reputation for being dangerous, with everything from rhabdomyolisis (exercise-induced kidney failure) to retinal detachment reported in the medical literature as possible side-effects. But these tend to be rare outcomes, and there’s no evidence yet that Crossfit is any more dangerous than other forms of intensive exercise. One study found that 70% of participants had been injured at some point; it sounds like a lot, but researchers estimated that the rate was three injuries per 1000 hours trained. That’s roughly the same as you’d get from gymnastics, and far safer than contact sports like rugby.
Still, there are some aspects of Crossfit which make it risky. There’s a big emphasis on high reps and heavy weights, and a lot of gyms care more about that than correct form. Since most trainers have only a weekend’s training in Crossfit methods, and no expertise in biomechanics, they’re often oblivious to small mistakes in technique which can lead to big problems in the long term. When you’re lifting half your bodyweight above your head, form matters.