The definition of a Tinok Shenishba and the status of today’s non-religious Jews:
The concept of a Tinok Shenishba is recorded in the Talmud and Rishonim, and is defined as a person who is an Apikores in his belief system or a Mumar in his Torah observance, but does not receive the halachic definition and severity of an Apikores and Mumar, and is hence not to be treated like an Apikores, being that he cannot be blamed for his heretical beliefs and behaviors. Now, for the definition of who enters into this category of people who cannot be blamed for their heretical beliefs, we find many levels, as well as debates amongst the Poskim.
A Jewish child who grew up in a home of heretics: The most basic definition of a Tinok Shenishba, which is not under debate, is a child who has been brought up in a home of heresy. This can be whether due to him having been kidnapped from a very young age by heretics or Gentiles and being brought up in their home, or due to simply being switched at the hospital and going home with the wrong set of parents who are Gentiles, or due to the fault of their parents, such as if the parents gave the child up for adoption to gentile parents, or the mother intermarried and the child was brought up in a Gentile home. In all these cases the child is defined as a Tinok Shenishba and not an Apikores even after he becomes Bar and Bas Mitzvah, and applies whether he simply has heretical beliefs or is brought up in a different religion such as Islam, Christianity, etc. and practices them.
A Tinok Shenishba who now discovers his Jewish identity and the Jewish religion: While the above definition of Tinok Shenishba certainly applies so long as the child does not even know that he’s really Jewish, it is debated in the Rishonim and Poskim whether it still applies even after he discovers his Jewish identity. Some Poskim rule that once the Tinok Shenishba is made aware of his Jewish identity and of the Jewish people and their observance of Torah and Mitzvos, then if he still continues in his ways of nonobservance, then he loses the status of a Tinok Shenishba and is considered like a regular Apikores. Other Poskim, however, rule that he continues to be considered a Tinok Shenishba even after he discovers his Jewish identity and the Jewish religion. Practically, the main opinion follows this latter approach. Furthermore, even according to the dissenting opinion which holds that they are considered like heretics, the level of exposure that is necessary for them to leave their status of Tinok Shenishba, is so high that today there virtually no longer exists any Apikorsom, even if a child was brought up observant and then went off the Derech. Furthermore, even if this level of exposure has been reached, the person retains the status of a Tinok Shenishba until he is properly given reproof for his mistaken ways, and hence since today people no longer know how to give reproof even if they try, therefore almost all nonreligious Jews today retain the status of a Tinok Shenishba. [These two later reasons can be used to justify the status of Tinok Shenishba even those who were brought up religious and then went off the Derech, so long as they have not had full and true exposure to the truths of Judaism, it’s philosophies, and its miraculous nature and given proper rebuke.]
Today’s non-religious Jews have the status of a Tinok Shenishba and not of an Apikores, due to one of the following reasons:
1. They were brought up in a home of heresy and hence can’t be blamed for their heresy and non-observance.
2. They do not have enough exposure to Judaism and G-d’s providence.
3. They are not given proper rebuke.
 See Sefer bIna Vadas 1; Pesakim Uteshuvos 240:49
 See Shabbos 68b; Avoda Zara 26a
 See Rambam Mamarim 3:3; Ramban and Nimukei Yosef on Bava Metzia 110a, brought in Darkei Moshe 159 and Beis Yosef Y.D. 159; Radbaz Mamarim 3:3; Shut Rabbeinu Betzalel Ashkenazi 3
 Shabbos 68b; Avoda Zara 26a; Rambam Mamarim 3:3; Ramban and Nimukei Yosef on Bava Metzia 110a, brought in Darkei Moshe 159 and Beis Yosef Y.D. 159; Radbaz Mamarim 3:3; Shut Rabbeinu Betzalel Ashkenazi 3
 Admur Ribis 80 in parentheses; Rama Y.D. 159:3 “and don’t know Toras Yisrael”; Shach 159:6 and 8; Ramban and Nimukei Yosef Bava Metzia 42a in name of Rabbeinu Tam, brought in Darkei Moshe 159:2 and Beis Yosef Y.D. 159; Radbaz Mamarim 3:3; Derisha 159:2; Shut Rabbeinu Betzalel Ashkenazi 3; 2nd opinion in M”B 385:1 regarding Karaits; Igros Moshe E.H. 1:82-22 and 4:59 regarding reform Jews; Teshuvos Vehanhagos 1:528; 2:564; 5:95; 6:90; Minchas Shlomo 2:4-10 and Halichos Shlomo Pesach 9 footnote 135; Bina Vedaas Miluim in name of Rav SZ”A; Betzeil Hachochma 2:76; Shevet Halevi 9:198; Yissa Yosef 3:97; See Piskeiy Teshuvos ibid footnote 22
 Admur Ribis 79 “A heretic Jewess who has a son from a gentile which is brought up like a heretic just like him, it is forbidden to lend him money with interest according to all opinions, as he is like a child who has been captured by gentiles and is not similar to a real Apikores which is defined as a person who knows his creator and intentionally rebels against him… However, this boy does not know. Now even though afterwards he discovered that he is Jewish and he sees the Jewish people and their religion, he nonetheless maintains the status of an Anuss [i.e. Tinok Shenishba] and according to all is not considered a rebel. Thus, according to all opinions it is forbidden to lend money with interest to Karite Jews, as although they are deniers of the oral tradition, they do not have the status of a Apikores. Being that they are not deniers due to their own will but rather due to the fact that their parents brought them up with this mistake and they are therefore like a Jewish child that has been captured and brought up with their mistake and is defined as an Anuss [i.e. Tinok Shenishba].”; Rambam Mamarim 3:3 “Even though the person afterwards discovered that he is a Jew and he sees the Jewish people and their religion nonetheless he still defined as a Anuss [i.e. Tinok Shenishba] being that he was brought up with that mistake. Therefore, it is proper for one to influence them to do to Teshuvah, and to draw them with words of peace until they return to the strength of the Torah.”; Beis Yosef O.C. 385 and Y.D. 159 regarding Karaits; 2nd and main opinion in Darkei Moshe 159:2 as rules Rambam and Beis Yosef ibid; 1st opinion in M”B 385:1 regarding Karaits; Chazon Ish Yoreh Deah 2:6, 16 and 28 and 62:21; Zekan Ahron 12; Binyan Tziyon 23; Milameid Lehoil O.C. 29
 This is the main ruling of Admur ibid; Chazon Ish ibid; Rebbe in Likkutei Sichos 2:273; 6:273; 15:198; 26:131; Toras Menachem 51:226; Hisvadyus 5748 4:60; 5750 Shemos p. 144; Mishneh Halachos 14 p. 59
 Igros Kodesh Rayatz 2:526 “A person is only defined as an Apikores if he denies the Torah and Mitzvos and in godliness due to his own foreign ideologies which are the result of deep philosophical thought, as was common amongst the philosophers in previous generations. However in our generation, even those who are completely unobservant r”l majority, if not all, of them are very distant from any deep philosophical and ideological understandings and rather are simply drawn after such opinions, and the lack of fulfilling Mitzvos, on the majority is simply because it’s easier that way for their life and not because heaven forbid they are intentionally rebelling and betraying G-d. Even their transgressions of negative commands is not in order to get G-d angry but rather simply to fulfill their lusts.” “; Chazon Ish Yoreh Deah 2:16 “It appears that the concept of Moridin [i.e. a real Apikores] only applies in the time that the providence of God is revealed, as it was during the times that we witnessed miracles which acted as a sign from heaven, and at a time where there were Tzaddikim of the generation who lived with open miracles that were viewable by all, as in such a case one who still maintains heretical beliefs shows that his intent is simply to rebel …. However, at a time that there is complete concealment of our faith…. Our job is to return them with chains of love and show them the light of the Torah as much as we can.”
 Hagahos Maimanis Deios 6
 Ahavas Chesed in name of Hagriy Mulin based on Maharam Melublin; Chazon Ish Yoreh Deah 2:6 and 28