Q:

Allowing persons having sars-cov-2 antibodies to move freely

Would it make sense from the public safety point of view to allow the persons already having the antibodies to move more freely than the persons not having the antibodies? Or it is more of an ethical question than a medical one?

A:

Projects for broad-based antibody blood tests are currently springing up like mushrooms.
But the first test series available will be needed for the staff of health care.
of course there are other interests for antibody tests: virological, epidemiological  and as your question implies economical. 
Antibody blood tests should provide information about the spread of the corona virus so that the measures taken by the authorities can be adapted. A nationwide initiative is now putting pressure.
https://www.sciencemag.org/news/2020/03/new-blood-tests-antibodies-could-show-true-scale-coronavirus-pandemic
For example, if a selected group of people were tested for Sars-CoV-2 antibodies every two weeks, the course of the epidemic would be clearly visible.
The interest, especially in business circles, is huge. Everyone urgently wanted to know where they were in the pandemic, who was at best already immune and could therefore probably move around and work safely again. 
https://www.srf.ch/news/schweiz/coronavirus-antikoerper-tests-ein-schweizweites-projekt-wird-aufgegleist
Such data could inform practical issues such as whether and how to reopen schools that have been closed. Relatively few cases have been diagnosed among children, but it isn’t clear whether that’s because they don’t get infected or because their infections are generally so mild that they go unnoticed. Testing children for SARS-CoV-2 antibodies should resolve that.
https://www.sciencemag.org/news/2020/03/new-blood-tests-antibodies-could-show-true-scale-coronavirus-pandemic
Authorities are still afraid of a roll back of the wave when people start moving freely again. It must have a great acceptance and also be respected by those who should still stay at home. 

