Yes, because that's how society works and is literally the whole point of the vaccination programme.
Let's simplify your question.
Do you want the people who cannot have a covid vaccine to be able to mingle with people for whom it hasn't worked?
Do you want the people for whom a vaccine hasn't worked but voluntarily received it to be able to mingle with those who are vaccinated?
Do you want those who are vaccinated to be able to mingle with anyone who isn't in any capacity?
Where would you as an individual draw the lines?
Subsitute covid for any other disease that kills people for which a vaccination is readily available. Flu? Measles? Should we segregate those people too?
Perhaps I'm over-estimating people's abilities to think bigger picture here, but let me repeat exactly what i said in my previous post: It's not about this example, it's not about covid, it's about what this may allow a government to do in future.
I don't think government should exist in anywhere close to the capacity it does anyway, so i'm probably wasting my time on this argument.
Edit: I just saw the last line in the attached quote. If i'm worried about other things throw away my phone and pc? I'm only allowed to be concerned about one thing at a time? What a blinkered world view. Shame.