In the case of diabetes, evidently causal.

The answer for cancer is far more complicated. First, while "cancer" suggest a uniform disease, every cancer type is a unique disease manifestation. Also, we need to differentiate between prevention of cancer and death from manifest cancer. I'm aware of only one study that investigated the question whether strength training post cancer diagnosis favourably affected survival. That study found some preliminary evidence in favour of strength training. A 2020 systematic review concluded that exercise training of higher intensity and volume (MST and cardio jointly and separately) favourably affects cancer survival and recurrence. But the data a re too limited to stratify by cancer type.

As far as cancer prevention is concerned, the data are inevitably observational .(unless you accept trials in rodents as evidence for humans, which I'm always a bit skeptical about)