Most in political science and international relations probably don't use 'realism' in any strict philosophical sense. Most here mean that politics and foreign policy should be analyzed and understood in terms of power and self-interest--so people are never motivated by ideals or moral values. I think if you want to succeed in the world, it helps to have a value system easily reconciled with your perceived self-interests.
Platonism and realism are not contradictory terms.
When Frege said that numbers were real but physically non-existent objects, he was also at pains to point out that numbers were not mental objects either. Numbers are non-physical objects that subsist in a 'third' realm. Because Frege's mathematics is independent of mind, he could be said to be a 'Platonist' and a 'realist'.
Meinong arrived at an equally rationalist and interesting position but one that did not reject the Kantian-Hegelian tradition. His position has been termed 'objective idealism'.
Yours, Charles Jannuzi