As to the recipent - medical compliance is a big deal post-transplant. If you're going to claim religious exemptions for the vaccine, what's next - religious exemptions to the anti-rejection medications you will have to take the rest of your life?
As to the donor - this is major surgery that harms a healthy person No medical facility takes that lightly. There are numerous layers of screening (and restrictions) before you are allowed to be a living donor. it is major surgery that is harder on the donor than on the recipient - and the donor will be in the hospital for a number of days. It makes no sense at all to accept a donor who is at increased risk for COVID for a multi-day stay, weaken the body by removing half of her liver which, for at least a short time makes them more susceptible to the ravages of COVID. Not to mention that the liver is one of the targets of COVID.
I should add that my sarcoma surgery at the Cleveland Clinic was one of a handful of times I had been in a room unmasked with people who were not members of my household. They removed it for surgery and I awoke, unmasked in recovery. So in addition to the damage the surgery does, there is also the potential for signficant exposure during surgery and immediatly after (especially in a hospital in an area with a high concentration of COVID cases.