There used to be issues with being fired if you were found to be HIV-positive. A landmark court case in which a New Zealand HIV-positive woman challenged her employer on firing her for refusal to take an HIV test sparked judicial review which deemed forced or mandated HIV testing to be unconstitutional. So as of now, teachers for the E2 and E1 visas do not need to be tested, but they should still take care because some schools still subversively test as part of health check-ups. It isn’t legal and if they are asked, they can refuse.