My parent's, who are in their late 70s and fully vaxxed and boosted. Love to entertain. Frankly, I think it is one of the things they love best in life, and their decision metric about risk vs. how much time they have left may be different than many, which I can respect. SO they are ready to get back to entertaining, and have on a small-ish scale. And their invites now always include, "if you are not fully vaccinated, please decline this invitation".
Of course it still relies on people to be honest, but I don't think there is anything wrong with include that. It doesn't shame people, it doesn't require them to announce they aren't vaccinated (they just say they can't make it and don't have to elaborate), and it makes other people feel more comfortable attending. And it also opens the door to "sorry, Susie but unless you guys get vaccinated, maybe we will see you some other time, but we are keeping this event to only those vaccinated, so everyone can feel comfortable." Might be worth mentioning this to family members who keep canceling because non-vaxed people accept the invite. It's easier to do it preemptively than to have to uninvite or cancel after the fact.
I don't think people need to do that, but I respect their right to decide who want in their home, under what circumstances.