I think there are a lot of misconceptions about this.
First of all, there are a whole list of infectious diseases that doctors are legally obliged to report to various government ministries. For the list see this:
https://www.moh.gov.sg/content/dam/m...20Apr%2013.pdf
These are purely for epidemiology and surveillance purposes. This is how every night on the News you hear reports on how dengue cases are on the rise or how HFMD cases are on the rise etc etc
This information is kept very confidential. It is not shared. It will not affect your job or job application even if you work in the civil service.
The only infectious disease the government will actually take any action on when notified is HIV. And the only action they will take is to very gently and kindly ask the patient to share his/her sexual contact purely so that the ministry can call these people on the patient's behalf and advise them to get tested. Honestly, I think this is a very good thing. It helps protect the patient's identity.
I have personally seen many people who came to get tested because they received this call from MOH. And some of them were truly positive.
Honestly that is all they do.
I understand that there may be conspiracy theories on the government taking this info and doing other things with it. That has not been my experience and I shall not comment on that. From what I have seen, the notification process serves a public health agenda only. So I really do not think you need to be too concerned about this.
If you still are, JB and Bangkok are good alternative locations to get tested.