Things are messier in the US where insurance is tied to an employer, and employers can implement arbitrary "optional" measures like requiring you to be a non-smoker or very strongly encouraging you to take a biometric screening so that you can "elect" to participate in their insurance plan. If you don't elect to, insurance options outside that through the exchange (healthcare.gov) are not great and often very expensive. It's a complicated subject here.

As far as the DNA sequencers, I haven't heard of any sharing their data with insurance companies today but I also haven't read their privacy policies closely to see what they could do. If 23andMe has the option to give you a copy without retaining any that might be the safest option here.