It is an old debate. I have been trying to come up with a clear cut definition. Rambam, of course, has his principals, but they dont really seem to be addressing the question that modern Jews have about being Jewish.
A “frum” or “orthodox” person is someone who accepts the Torah laws as interpreted by Talmud/ Shulcha Aurach. If they dont follow them because they have a compulsion to break them, or they do not feel ready or if they dont know about them, then they are still orthodox. If they reject the validity of the laws, even if they go through the motions, then they are not orthodox.
Does that work?