1. Yukio could be Bombay blood typeBlood groups are based on proteins that are found on the outside of your blood cells, which your body uses to tell that those cells are you and not bacteria or something. People with the A allele make the A protein, B makes the B protein, and O makes neither. AB is when you have an A allele and a B allele and make both proteins at the same time.
A and B proteins are both made out of another protein called H. The A and B genes give different instructions for what to do with the H protein, so you can end up making it into two different proteins. O is basically a broken A gene that doesn't do anything; your cells have H protein but then can't make anything out of it.
But some people are missing the gene that makes H protein in the first place. That's called the Bombay blood type. So they can have all the As and Bs they want in their genes, but without any starting material they aren't going to make any A or B protein, and most common blood tests will come up O. This is recessive, so Neuhaus and Yuri could both be carriers of the Bombay blood type without having it themselves.
AB, Hh (Neuhaus) + ??, Hh (Yuri) = ??, hh (Yukio; appears to be O regardless of actual ABO group)
This theory is probably dead if Yukio ever gets a successful blood transfusion from someone, since people with Bombay blood don't recognize H protein and get bad reactions to A, B,
and O blood, which all have H protein and/or the As and Bs they made from it. So they can only get transfusions from other people with Bombay blood. Bummer.
2. Neuhaus could be Cis-AB blood typeUsually people with AB blood got the A from one parent and the B from the other, because there's only one chromosome with one copy of the ABO blood type gene, and you get one from each parent. But sometimes DNA gets mixed up when cells are dividing and you end up with both an A gene and a B gene on the same chromosome. So that person gets the whole AB package from one parent and then can carry any blood type on their other chromosome. So Neuhaus might have an O gene to pass on after all:
AB/O (Neuhaus) + A/O (Yuri) = O/O (Yukio) + A/O (Rin)
This is more common in Korea and Japan, if you pretend for a second that 1 in 100,000 people could ever possibly even once be called "common." Good enough for a crack theory!
3. There could have been a random mutationThe O version of the blood type gene is a very slightly mutated A that doesn't make any A protein. Random spontaneous mutations that just happen to do exactly what your crack theory wants are
really rare, but it would only take one small mutation to turn Neuhaus's A gene into an O for Yukio:
AB (Neuhaus) + ?O (Yuri) = OO(<--fresh mutant A)