Things may have changed but there is no address on my Birth Certificate, but OP, you have heard that someone is planning to misuse your address, which if this misuse involves a notification to the registrar, or any other felony.
You are obliged to report knowledge of a pre-meditatied crime to the relevant authority and to the police, so start phoning.
The registrar will no doubt be willing not to inform the person who states your address that he or she has been warned by you.
You cannot be held responsible for wrongful information that others give, but you can be held responsible for not informing the authorities that it has come to your attention that someone is considering doing so.
And, if you take no steps, you could be deemed to be complict in this use of your address.