Disclaimer: I'm practically a Willie, except younger. I have received a living-donor transplant, and now know a bit about the whole process. Although the details vary by region, the general process is the same.
TL;DR;
- It's not at all difficult for two random people to match to a satisfactory degree, for renal transplantation, at least.
- The real problem is eligibility of the donor and receiver to donate or receive a kidney, considering the risks of a complicated surgery.
- When I watched the movie, especially the ineligibility of Albert to donate came across as laughably unrealistic.
Firstly, let me say as a preamble, that there remains a lot to be improved regarding transplantation in general. Kidney transplants are the most common and therefore most studied transplants, and there are lots of extra complications associated with other transplants. However, if we knew the exact details of even making kidney transplants lasting, the so-called long-term rejection wouldn't have been incurable, and transplanted organs wouldn't have had, essentially, an expiry date.
My point being that it's possible to provide some insights as to whether or not Willie's case is likely, but I'm wary of using phrases like "there is no way . . . ".
The experiments
Paulie_D's answer goes into enough detail about the 'matching' lab tests. From anecdotal experience, I have never encountered people that have a problem with those though, as long as blood types match. Kidneys from closer relatives than a random stranger tend to last longer, but generally there are so many important factors affecting the success of it all, especially the lifestyle the receiver chooses after transplant, so it's not a word of God.
Where I live, as long as the most important factors (The blood types A, B, and O, and the rhesus antigen) match, the minutiae of the Panel-reactive test are usually not too significant, because they tend to match as well.
As far as I recall, the default in the cross-match test is that there is no match, which means the white blood cells won't pick up the antigens on the transplant organ cells. In this test, it's not that they would attack unless we're lucky, it's that they normally won't attack unless we're unlucky. I could be wrong about it, though bear in mind that the nine donors I met all had 0 of the 18 'problematic' antigens that would match.
Personally, I was one unlucky candidate, and it didn't work out with eight different donors before the ninth did (they went through the blood type filter first), but the hurdle wasn't the cross-match test, or the Antibody test, but that the donors were ineligible.
The devil is in the details of the full check-up. The receiver, or the donor, may be ineligible for a myriad of reasons. My donation candidates were all young, yet a single metric in each would've meant they were bound to get into trouble if they donated their kidney.
There are also other tests, like a checking of veins for anatomical compatibility, but they're often not critical to the possibility of transplant.
Transplant, the better option
To need transplant in the first place is an entirely plausible and real situation. It's not necessarily because of kidney failure per se (There are patients on dialysis who were born without kidneys), but because of the worsening condition. Dialysis helps keep the levels of bad things in blood in check (most importantly, BUN and creatinine), but considering they're usually products of complex metabolic reactions, it's possible that their levels spiral out of control for unknown reasons. There is also balances like phosphorus/calcium in blood, and dialysis is usually very ineffective in getting rid of excess phosphorus.
Patients are also usually just 'better off' with a transplant, even mentally so. Transplant patients, especially elderly ones, have a longer life expectancy than if they remained on dialysis.
Willie's eligibility
This is one part that drifts a bit away from realism. All the benefits of transplants aside, things are a bit tougher for a receiver, since they have to endure
- Surgical wounds (depending on the method, may be large or relatively small)
- The presence of an alien organ (they have to make up space, this is not too much of an issue for kidney transplants usually)
- Heavy immunosuppressive drugs with typically dire side effects
It's therefore not unreasonable that a transplant receiver may be considered ineligible for a lot of seemingly unrelated reasons, including old age. This article discusses the mortality rate for transplant patients older than 60. In some jurisdictions, these factors are considered so seriously that surgeons may outright refuse to perform transplant.
Willie's doctor was way more likely to adjust his dietary plans further, or increase the dosage of some of the medication, or dialysis intervals. It's much safer, if a bit more depressing and painful for Willie. There's also the fact that even if he didn't like dialysis, he didn't mind it either, from a mental aspect. IMHO, it was a tool to incentivize Willie and drive the plot further, and not strictly realistic.
Albert's eligibility
This one drifts away so drastically it's Fast 3. First off, you can't ever stop hearing this from the professionals in the field: "Well, what does an old kidney look like, anyway?"
The two most important factors damaging kidney health are old age, and poor lifestyle habits that tend to ultimately lead to high blood pressure or diabetes. Albert doesn't strike me as the most glaring example of success in either regard. Him donating his kidney is like donating the overused battery of an old laptop. It's very unlikely to be of much use to Willie.
Not only is it going to be of little use to Willie, it will end up posing health risks for Albert too. The main caveat for a living donor is, well, that they lack a kidney! They would need to monitor their blood pressure and stop eating salty or very sweet food. It would be very possible that, a year from transplant, Albert would need dialysis or transplant himself.
Young donors don't usually get into much trouble if they don't smoke, or drink alcohol. Poor nutrition could cause trouble in old age just like good ol' Albert, but this part would have made much more sense if there was a sacrificial son who just repaired his relationship with the father throughout the movie, and who found himself guilty for neglecting the old man's condition, maybe?
