I'm not a doctor but my father has had to undergo several platelet transfusions during his cancer treatment so I do have some knowledge. Side effects of platelet transfusions are usually mild and rare because doctors take care that the right platelets are used. If severe side effects do not occur, doctors continue with the transfusion because low platelet counts are far more dangerous than the risks of minor side effects from the transfusions.
Those undergoing chemotherapy often suffer from low platelet counts and transfusions become necessary sometimes. It's important to get the platelet count high as soon as possible.