It depends is the answer - in the cited case of Pimlico plumbers for instance, they have to go into peoples homes, some who will be immunocompromised eg on chemo, very elderly, plus people who cannot be vaccinated for medical reasons, so their employer wanting them to be vaccinated is fair enough with medical exemption for those who cannot have any version of the vaccine.
Airlines similarly need to protect their customers and crew who need to be at close quarters for hours, some of which may for medical reasons be unable to be vaccinated so the rest of us need to be vaccinated to protect them. For cruise ships it's a no brainier. You don't have to travel, it's a choice
I cannot imagine shops demanding it, restaurants etc it's unlikely but they cannot afford to be closed again and if that means barring refusers it might be worth their while