Perceptual hashes are reasonably robust to small perturbations. Scaling and converting shouldn’t be a problem, though applying filters that change the colors or blur the lines might.

If it’s been changed enough that it hashes to a different value, then it might be reasonable to treat it as a different image. At some point a human is also going to say “that’s not the same.” You can always change your hashing algorithm if you find it’s missing too many dupes.

Regardless, for the domain we’re talking about (deduping training data), a few false negatives should be acceptable.