So I read the article last night. Here are the points that I got out of it.
1. Organ rejection is an immune response which the body initiates when it identifies "forign" material.
2. If a baby is breastfed they are exposed to the mother's antigens early in life and their immune system becomes hyporesponsive to them.
3. If that baby (once grown) then has an organ transplant from someone who has those same antigens (someone related to them maternally) they are less likely to reject the organ.
4. There isn't enough evidence to say whether or not it matters if the donor is also breastfed as in most families all children from the same mother are breastfed (in the study there were only 2 out of 39 where the recipient was breastfed and the donor was not therefore statistical significance couldn't be shown).
All in all another fabulous reason to breast feed your children, but it doesn't change your basic genetic makeup.
Everything will be ok in the end. If it's not ok it's not the end.