Anesthesia impairs the electrons transport in your brain, effectively ending that thread of consciousness, and, depending on the procedure, your brain can be altered by chemical/oxygen saturation changes. You wake up very subtly different, but most people are ok with that.
People have strokes or accidents and wake up missing memories and with changed bodies, but their families still call them by name.
You still being you is a matter of degree, not a binary, and different people are comfortable with different degrees of change.
I wouldn't call that degrees of change but degrees of damage. The thing is, past a certain degree of damage people stop having opinions, so how would you know the individual is comfortable with it?
In this case, the damage is total. The degrees end here, it reaches a binary state: from alive to dead. And then something else entirely says they are the dead person and they are alive.
The question is, does society accept a complete switcheroo? The individual died in the process, they cannot give an opinion on this. The copy is another entity. There are no degrees, it's all absolutes with this process.