I am a convert and have learned both opinions. My late Rav, Rabbi Gedaliah Anemer, zt'l, held in accordance with the Rema. I did not sit shiva for my father or say the kaddish for him. However, Rabbi Yitzhok Breitowitz, shlita, told me that because there are "chashuvah" poskim who hold otherwise, e.g. Rav Ovadiah Yosef, the response should be based on whether my biological parent would appreciate it if he/she knew that I was saying kaddish in their memory. When Rabbi Maurice Lamm republished my Baltimore Jewish Times story of my own conversion, in his book "Becoming a Jew," he cut out my statement that I could not sit shiva or say kaddish for my parents, either in recognition of the controversy, or because he disagreed with the opinion.