That's the purpose of new strains. As Bibi just said for Israeli's, we'll need to have boosters every 6 months.
People that had had the virus before there were any tests available for it, and thus are immune and need no shots for it, would not be able to prove they were immune and not needing the shot, if antibody tests could not detect antibodies properly.... .
Question is, how far back can those antibody tests check?