My guess is that most people would not be okay with that and choose to opt out.
But my question/argument is, would that be a rational decision? I don't see a lot of benefit for the customer to deny the store those options, so why do it if there's nothing to be gained from denying.
> attempting to stitch your actions on the internet to store visits to more effectively sell advertising
I think this is the key factor. If people see themselves as susceptible to such manipulation, then it does benefit them to deny such behavior to prevent stores from affecting them negatively.