Final answer:
The symptoms and findings in the Irish Setter suggest a Babsia infection, which is a protozoan parasite causing these clinical signs. The identification of the parasite form in the red blood cells and specific diagnostic tests can confirm the infection.
Step-by-step explanation:
The presentation of pale mucus membranes, an enlarged spleen, and icteric appearance of the skin in this Irish Setter, coupled with the observation of basophilic organisms within red blood cells on a stained blood smear, suggests an infection with a protozoan parasite. Given these signs and the morphology of the organisms identified, the most likely protozoan responsible is Babsia. This diagnosis would be consistent with the presence of intracellular trophozoites in erythrocytes. To confirm this, specific diagnostic tests such as Indirect Fluorescent Antibody (IFA) or Polymerase Chain Reaction (PCR) can be used to detect antigens or DNA of the pathogen.