This is actually a good idea. If they are legit, they should be willing to identify themselves, but they wont be happy about it.

I would ask them what info they have on you, who gave them permission to access it, etc. Tell them no personal info, even name. They can look it up for free online if they have becon(or similar), but why help them? Tell them you don't want to be on any lists, and them doing so is a state and federal privacy violation. You have their info so you will hold them personally responsible for the violation.

Also, they may be in violation of medical privacy laws just for asking about your vax status, so friendly advice they may want to rethink this career path.

Finally, they were not invited, point to your no solicitation/trespass siarn, say they are not welcome, and their presence is unsettling. They should leave immediately and not come back. If they dont leave you will call the cops. If they aren't gone in 1 minute you will consider your life and property in danger and will put them under citizens arrest and/or open fire.

Your bases are now covered.

.

FYI in my area, there has been a rash of breakins and arson. Strangers coming onto property uninvited is what is happening. One or two distract the homeowner while the others sneak around back and break-in.