The phrase “non-observant Orthodox” was commonplace in American Jewish circles in the mid-20th century, when it described a significant share of the Jewish population. If it has fallen into disuse, that is because, Zev Eleff writes, the type has largely vanished from the American scene:
Decades ago, . . . it was well-known that Orthodox life and Jewish law could be decoupled, no philosophical apologetics needed. This sort of sociological separation yielded a variegated Orthodox profile. . . . The non-observant Orthodox Jew emerged as an indispensable member of the Orthodox community, supporting its institutions and preempting those who would have preferred more rigid definitions for Orthodox Jews. True, the non-observant Orthodox Jew was by and large removed from Orthodox Judaism’s inner circle, but was also far from being an “outsider” in this community. . . .
Halakhah was not an all-or-nothing arrangement for this group of self-described Orthodox Jews. On the one hand, [they] made no claim that they abided by all the strictures of halakhah (although they did feel that the rabbi ought to sport an unimpeachable record). On the other hand, these laymen contended that this did not disqualify them from the ranks of the Orthodox. Certainly, they did not agree with the theological points of view of the Reform and Conservative rabbis who preached from pulpits and filled editorial columns in the Jewish press. [Yet] they did not frequent the synagogue all that often, behavior that was more closely in line with the non-Orthodox rank-and-file. But when they did make it, say, to recite kaddish or for a bar mitzvah, their choice was invariably the Orthodox variety. . . .
The more homogeneous character of the Orthodox community [that has emerged more recently] has . . . contributed to an increasing sense of rigidity. . . . Orthodox leaders have tended in the past few decades to pay more attention to what ought to count as “Orthodox” and to patrol community borders [more strictly]. The “non-observant Orthodox Jew” has been eliminated from the lexicon.
Read more on Lehrhaus: http://www.thelehrhaus.com/scholarship/2017/6/7/the-vanishing-non-observant-orthodox-jew