The Hagada tells us regarding the Rasha, "U'Lfi SheHotzi Atzmo Min HaKlal Kafar B'aIkar", because he removed himself from the tzibur he is a Kofer. Rav Isser Zalman Meltzer asks shouldn't it say the opposite way around, since he is a Kofer he has removed himself from the tzibur?
He answers with a story from his Rebbi, Rav Chaim Soloveitchik. A person who had left the Torah way came to Rav Chaim and said that he had a number of questions about Judaism. Rav Chaim said to him that if he has questions, he has no problem to answer them for him. However he doesn't really have questions, he only really has answers. He has answers and excuses why he has left Yiddishkeit, cloaked in the form of questions. However he left Torah because it was convenient for him and he merely concocted the questions to justify his actions. Questions like that can never be answered to the questioners satisfaction.
This is what the Baal Haggadah says about the Rasha. Since he has chosen to remove himself from the tzibur that keeps Torah in order to chase his heart's desires, therefore he is Kofer BaIkar. His Kefira is only a justification for separating from the religious way of life and is not a real theological issue.