They might or might not, but it will be an opportunity to show up at your door and ask if each of you had a shot and can they post a BLM sign in your yard because who doesn’t support BLM?
If you give them a hard time then they know who did not get the shot. They can tell you that someone from the health department will be around to talk to you later.
If you say that you did have the shot, they also win. They are also happy with conditioning you to lie.
You could shout through the door, “Can’t open the door! I think I may have Covid!” and watch them run away through the peephole. Under your breath you can actually say, “I think I have Covid [fools at the door]” so you aren’t lying.
3rd option is to not answer the door at all.
Didn’t say ‘yes’ or ‘no’.