A more useful way of thinking of "natural rights" is that "The set of rights that, if everyone were to have, would maximally smoothen interaction between individuals and groups."
I don't think there's a real argument that, somewhere in our DNA, exists a list of personal freedoms every human being ought to have. Feels like an ad absurdum more than a genuine engagement, tbh...
I seriously doubt that genetic research will ever find natural rights. These were created by philosophers, revolutionaries, soldiers, and all manner of other freedom fighter. They were not given to us by our genes, they were created by us.