"Orthodox" is just a word and you can give it any parameters you want. But one thing is certain - "Shabbos, Kashrus and Taharas HaMishpacha" are not it. These 3 Mitzvos do not comprise any particularly unique set. Shabbos obviously is unique in that someone who publicly violates it is considered outside of Klall Yisroel regarding many things, but Kashrus and Taharas HaMishpacha do not, in and of themselves, convey any particular status on their practitioner.
In other words, if someone does not keep Taharas HaMishpacha, he is a sinner; but no more or less part of Klall Yisroel than someone who eats Chometz on Pesach for example.
If there is any minimum threshold for observance that causes you to be considered part of Klall Yisroel, it is the 13 Ikarim. It is Emunah. If you have Emunah then you are considered Jewish in all respects. You may be a Rasha, but you have a share in Olam Habah and you are considered part of Klall Yisroel.
If on the other hand, someone does not believe in the 13 Ikarim, then he is not considered part of Klall Yisroel. he retains the obligations of a Jew but incurs no benefits thereof. There is no Mitzvah to love him; there is no Mitzvah to return his lost objects; he gets no share in Olam Habah. More: Even if he does a Mitzvah he does not get credit for it, because he does not even believe in Mitzvos! if he makes a Bracha, you should not answer Amen, because it is not a Bracha. See here for more details.
And yes, what a person does, contributes to what he is, but -- what a person values contributes even more. A person is judged more by what he values than what he does. As the Posuk says: מַצְרֵף לַכֶּסֶף וְכוּר לַזָּהָב וְאִישׁ לְפִי מַהֲלָלוֹ. "A person is judged according to what he praises."
So if you have two boys in Yeshiva, boy A learns more than boy B, but he is impressed and awed by someone with money or some famous movie star or ball player, whereas boy B learns less but is more impressed and awed by a Talmid Chacham or a Tzadik - then boy B is a bigger Ben Torah than boy A.
One more thing: If a person willingly violates the Torah, he is a sinner; but if a person willingly disagrees with the Torah, then he is a heretic. So if a person says "I know that mixed swimming is wrong, but I give in to my Taavah and I do it anyway, and I hope that one day I will become stronger and stop," that person is a willful sinner. But if he says "I know the Halacha says its prohibited but I don't think that mixed swimming is a big deal," then such a person is disagreeing with the Torah, which makes him much, much worse than the first guy.
It's like if someone is caught speeding. if he tells the judge "I was speeding. I had no excuse" the judge will find him guilty. But if he says "I don;t agree that speeding is wrong," the judge will hopefully throw the book at him.
The first guy is a law-breaker; the second guy is a revolutionary. Big difference.