Absolutely nothing.
The DNA records aren't the type that can be used to clone you, or frame you with some kind of non-existent DNA copying machine.
They are autosomal records. (or similar genealogical, or non-medical, types)
The people spinning fantastic fairytales about how the jackbooted thug of big brother is going to crush your throat probably don't even know what autosomal means and no amount of eduction will convince them.
I encourage everyone to submit their Autosomal DNA to public databases. You may bring closure to someone who has been or known a victim of a horrific crime and there is no risk to you.
You have at least one reply about insurance companies using this information to screw you.
1. This type of information is practically useless, actuarially, and
2. It has been illegal for them to do so for many years.