The case of mammography is often brought up for this argument, but is a cherry picked example. Furthermore, it isn't a blood test, so it isn't even what is being argued against by fivethirtyeight.

There is no harm done by extremely accurate testing for HIV. and less accurate tests should be used in screening by medical professionals that know how to proceed from a positive result. Again, blanket statements like "We Don’t Need More Blood Tests" are dangerous