Doesn’t feel like an unsolvable problem, certainly not one without edge cases but surely we can hit 80/20 without too big a hassle.
Doing low-hanging fruit isn't enough here. Honestly I just don't feel like the time is right to build such big DNA databases yet. Maybe one day with quantum encryption (can't observe the state without modifying it) or whatever else we may figure out, but today it just seems like you're taking a risk for yourself and half a dozen layers of relatives
2. Send a postcard to the billing address where you signed up (verified against credit reports) with a one time verification code, upon which some second factor is set up. Maybe put 20 "rescue codes" on the postcard too, if you like.
3. Force user to enable some sort of second factor authentication on their next login.
23andme bears responsibility more than users like banks bear more responsibility for customers choosing stupid pins. DNA info is valuable they need to design good safeguards.