There are several cases of people who identify as "Orthoprax", meaning that they follow mitzvot, but do not believe in G-d. (Most notable have been the cases of anonymous rabbis like the aforelinked one, who's congregations don't know they are closet atheists).
Halacha treats secular Jews, who don't keep Shabbat, etc., differently in many matters (for example, with kashrut). How does halacha treat someone who does not believe in G-d, but fulfills the mitzvot (almost the opposite of Reform Jews who believe in G-d, but don't fulfill mitzvot)? Does it make a difference when an apikoros is shomer mitzvot?