Should a person with blood type O accept an offer of a blood transfusion from someone with blood type A? Why or why not?

No, they shouldn't because they're incompatible

Explanation:

Compatibility among blood groups is given by the presence of antigens in the red blood cells, those are controlled by genes that can be either allelic or linked by proximity in the same chromosome. There are 33 blood groups system and approximately 300 antigens. The grouping is based on patterns of reaction in antisera testing. The most relevant blood groups systems for compatibility are:

ABO system: Refers to the presence of antibodies in the serum; A have antigen A and contains antibodies against B; B have antigen B and contains antibodies against A, O doesn't have antigens but contains antibodies against both, and AB have both antigens but doesn't contain antibodies

RH system: Rhesus system: Indicates the presence or absence of the immunogenic D-antigen, as RH + or RH-.

Based on these concepts, an O donor can only accept O blood type, because it has antibodies for either A, B or AB, and transfusion will trigger immunological response, however, O blood type can donate to either group.