Considering how easy it is to get ahold of someone else's DNA and the potential advantages of genetic testing, I think it makes more sense to push for anti-discrimination laws instead of avoiding genetic testing.
I don't deny there's a problem, but this is at best a several-year stopgap, not a solution. You will want them to sequence your DNA to determine which cancer drugs will work best when you are sitting in an office with cancer.
The problem is that medical insurance is currently uncomfortably between actual "insurance", coverage for unknown and expensive catastrophic events, and "health care", a program for spreading the costs of health care between many people to equalize the burdens and also sort of cover the insurance use cases. Expanding our knowledge of what you might get starts breaking down the premises the insurance system is based on.
Sure, you can lie. But god help you if you ever need coverage [even for a non-related disease] and the insurance just flat out won't cover you.
I for one rather don't know and don't. One of the major reasons is exactly the one described above.