They are citing ONS figures of excess deaths as proof the vaccines are killing people. I tried to explain that not being able to get a doctor’s appointment, staying home and getting fat, etc explain the figures (official sources have said it too) but they said it’s “gaslighting” and then said their family doctor wouldn’t get the vaccine.
A lot of people are saying cut them off, but I have a family member who was into the anti-vax conspiracy theories and kinda still is, but it’s much less of a focus now and is pretty obviously just being carried forward by cognitive dissonance at this point. There will never be total victory, but there can be a reasonable truce.
What I’d suggest is the most counter-intuitive strategy - show genuine interest. Say “Ok, I want to know more, but I need you to be specific. Tell me what your theory is and what the evidence is, I’ll take my time looking at it, and respond in detail.”
Keep in mind, they probably won’t pay attention to whatever your respond with. That’s ok. The response isn’t the point, pinning them down on what they think is. So often these things are purely emotional, and forcing them into a logical framework will make them do the work for you. As for the response, odds are it’s some combination of cherry-picked data and spurious correlations, if not outright made up facts. Think of alternate explanations for what they’re showing you that are more plausible than a vaccine killing people. And remember that if the vaccine really was killing people, it would be really obvious, not something we need look deep into the matrix to find.