I'm wondering why can plasma be administered to anyone without concern about a transfusion reaction?

See below. There are transfusion reactions related to plasma blood products including the most common cause of transfusion related fatalities in USA and Canada called TRALI(transfusion related acute lung injury), other reactions include anaphylaxis, TACO(circulatory overload) Plasma may contain antibodies(anti-A and B, anti-HLA, anti-HNA) proteins (IgA). See FDA website with more info: http://goo.gl/He8eQ7.
Lack of cells. The reaction of the body to foreign bodies and have transfusion reaction depends on the presence of offending allergens or that which incite reaction and the presence of receptors in the cells. Plasma would remove the cells and only the important components are there and no ABO or other systems will be triggered.