You're confusing mandatory public health level screening with opt-in personalized screening. The former is questionable at best - genetic diseases have very little external consequences, just the family / individual might suffer. Any argument about external consequences to neighbors/taxpayers slides us right into the dystopian future you'd like to avoid.

OTOH, we should have off the shelf genetic testing that sends you an SD Card / email and then deletes /anonymizes the results thereafter. You could bring that to a doc when you wanted to, and read the full results yourself. Very little harm in that aside from a de-anonymization campaign.