Organ cloning - possible to make a non-antigenic organ?
I'll contradict the answer posted here (ages ago) and say no, it isn't possible. Growing an organ wthout MHC proteins might be achievable, but it would be rejected for not having MHC1. NK cells instruct all cells without MHC1 to perform apoptosis. In this case, MHC1 antigens are required on cells for proper self-identification.

Keeping MHC1-less cells alive could be achieved by


equipping them with whatever is keeping erythrocytes and thrombocytes (also lacking MHC1) from being destroyed on sight. (A good idea, but see next paragraph)
disabling their apoptosis mechanism (Cells with disabled apoptosis mechanisms are commonly referred to as cancer, so we might want to not do this.)


MHC1 also has a function; it presents "peptide shreddings" from proteosomes to T cells; this way T cells can check if the cell contains internal foreign proteins (sign of a virus infection or cancerous transformation). Thus, removing MHC from the cells would make them very liable to become nearly unstoppable virus factories or tumor cells.

(On a side note, while everyone technically can receive 0 Rh negative blood, group-identical blood is used always, except in rare emergency cases. A and B antigens here, as far as I know, do not have function.)