I don't know why people think that DNA is so personal and private. it's the equivalent of IP addresses for biological beings.
Even so: processing IP-addresses is not allowed in general, in the EU at least. You need permission or a specific, allowed goal.
In the US many states collect DNA samples at birth, as well as for citizens born abroad.
If having the wrong IP address costs $1k extra per month, but only of other people know, then you'd also be more careful about keeping it a secret.
In America they cannot. This is forbidden by law.
... But they should be allowed to, you are more risky to insure. Just like under 25-yo's are more prone to accidents; or coastal houses are more prone to flooding.