אם-יהיה נדחך בקצה השמים, משם יקבצך '' אלק ה ומשם יקחך Roughly: Even if your dispersed ones are scattered to the ends of the heavens, from there HaShem will gather you and from there He will fetch you.*
In other words, no matter how unobservant a Jew may be, HaShem still will bring the person back - no qualifications, no restrictions.
"Observant" is not a synonym for "orthodox" or "haredi" and it's a variable value word. One is "more observant" and another is "less observant" than a third person, but all are Jews.
It upsets me to hear/read that a Jew feels "not good enough to be considered a Jew."
According to the rabbis, even the Jew farthest from the religion can "come back" on his dying day. That doesn't mean to wait until death is at the door, but it means that "once a Jew, always a Jew" even if some won't accept their fellow Jew because of past transgressions.
Even as we wandered in the wilderness, when someone was removed from the encampment - think about Moses' sister Miriam who was banished from the camp for her evil tongue (yes, I too wonder why Aaron was not cast out with her) - the banishment was only temporary.
Even a Jewish murderer condemned to death remained Jewish and the body was treated as a Jew's body.
A Jew who sits in a restaurant window eating roast pork and lobster on Yom Kippur still is a Jew; he might be denied honors in congregations that know him, but no one will deny he's a Jew (no matter how much we might wish to disassociate ourselves from the person).
Consider HaAhar (The Other **) who was an absolute apostate to science and philosophy. Despite his abandoning of faith and friends (among them Akiba ben Yosef) and students, including Bruriah's husband, Meir Ba'al HaNes. ***
Going from heloni - non-observant - to observant can be a steep path. Like mountain climbing, a novice should not attempt to scale Mt. Everest on the first outing. A person needs to "work up" - little by little - to greater levels of observance. Going "cold turkey" and trying to perform even half the mitzvoth usually ends up with the Jew giving up and returning to the heloni ways.
Even if the best intentions fail to reach fruition, the Jew still is a Jew.
Payot and gartel do not make a Jew. Neither does a פאה (wig) make a married woman Jewish (indeed, the late Ovadia Yosef said that a man should divorce a wife who wore a wig).
There are things that separate some Jews from others; e.g., the fellow eating pork and lobster in the window on Yom Kippur, but there is nothing that can separate the Jew from being Jewish in the eyes of Judaism.
A few words from פרקי אבות (Ethics of the Fathers) which we read starting with Shabat Hol HaMoed Pesach. At the very beginning, we read
which, as translated by The Mesorah Heritage Foundation reads: As it is said … And your people all are righteous; they shall inherit the land forever.
The explanation, from Teferet Israel, explains:
The mishnah refers to the world to come since in this world not all Jews are "righteous." In the world to come, however, all Jews will be deemed righteous.
So even the "rasha" sitting in the restaurant window eating pig and lobster will be righteous - if not now, then in the world to come.
Bottom line: If any Jew says they are "not good enough" to be a Jew, tell them שטויות! - and let them look up the word.
* Translation from Hebrew/English Sedur Kol Yaakob according to the minhag of Aleppo (Syria). If anyone knows of a Hebrew/English sedur following Moroccan minhag (tradition), please let me know - yohanon dot glenn at gmail dot com .
** Elisha ben Avuyah, 1st/2nd century CE tanna; mentioned once in the Mishna Avot (4.25) a truism: He who learns when he is young, to what may he be compared? To ink used on new paper. He who learns when he is old, to what may he be compared? To ink on used on blotted (erased) paper. Ben Avuyah also is mentioned in Mo'ed Katan (20a) discussing mourning rules. (Source: Masters of the Talmud, Alfred J. Kolatch.)
*** Source: http://tinyurl.com/kh3u34l