Blood type doesn’t impact compatibility among partners in any way, neither does it play a role in making a marriage healthier.
One of the only other reasons (besides human curiosity) you may want to know your partner's blood type is for transfusion and pregnancy purposes. Certain blood types can only give or receive to/from other blood types. This would be helpful to know in emergencies.
If you plan to have a biological child then compatibility of the RH factor of the mother and the child is important. If the mother is Rh positive and the baby is Rh negative, it can cause formation of antibodies that can attack the baby’s red blood cells. But don’t worry, this can be treated with Rh immune globulin prescribed by the doctor.
So why is there a belief that blood type has got anything to do with compatibility in marriage?
Well, in Japan, there is a blood type theory known as ketsueki-gata. This is the belief that certain blood types can be a clear indicator of someone's personality. But this theory isn’t scientifically proven.
For example, if you have type O blood you are seen as someone optimistic. Type AB, eccentric. Type A, well-organized. Type B, selfish.
By this theory, certain blood types will go better together than others. A female A works best with O and A males, a B female works best with O males, and an O female meets her match with an O male.
(For an even deeper dive into whether you and your partner are meant to be, I suggest reading this article ‘Tips on Determining Relationship & Marriage compatibility’)