Is that what’s going on with organ matching?

Abo is a major part of organ matching. Abo has to be considered for any organ transplant. Every organ differs but HLA antigens is a different, more complex set of antigens that needs to be matched to some degree as well. Abo is usually a simple test, so hla antigen matching is most of what "organ matching" labs spend their time on. I work in this field.

Yes, but even more complicated.