That's another vector, and everyone considers separately. But at least here one can - hypothetically - have a BAA and zero-retention agreement with Anthropic. Which means they have moderately strong incentives to wipe your data after a fairly short while. CLIA, if I don't misremember, mandates a few years at minimum.
It's not impossible: Claude can take care of bioinformatics part. But to understand genetics and cellular biology you need a knowledge foundation first.
Unless you just want it on a level "Does this mutation leads to a genetic disorder X" - this is a simple way to put it, but not enough to actually understand genetics.