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of, relating to, or conforming to the approved form of any doctrine, philosophy, ideology, etc.
of, relating to, or conforming to beliefs, attitudes, or modes of conduct that are generally approved.
customary or conventional, as a means or method; established.
sound or correct in opinion or doctrine, especially theological or religious doctrine.
conforming to the Christian faith as represented in the creeds of the early church.
(initial capital letter) of, relating to, or designating the Eastern Church, especially the Greek Orthodox Church.
(initial capital letter) of, relating to, or characteristic of Orthodox Jews or Orthodox Judaism.
Contemporary Examples

Patriarch Kirill of Moscow, the head of the Russian orthodox Church, went ahead with an official visit to Damascus last month.
Why Is Russia Supporting Syria’s President Bashir Assad? Owen Matthews December 1, 2011

orthodox Jews have voted Republican in every presidential election since 2004.
Collapse Of The American Jewish Center? Peter Beinart May 6, 2013

Even so, orthodox Christian pastors have not singled out gay weddings in the way that the people backing these bills have.
Conservative Christians Selectively Apply Biblical Teachings in the Same-Sex Marriage Debate Kirsten Powers, Jonathan Merritt February 22, 2014

My millennial friends have waited in line beside a cluster of orthodox women in long dark skirts to be seen by Peggy.
New York’s Sexiest Kosher Corsets Emily Shire August 19, 2014

“From 17 to 82,” said an orthodox subdeacon named Richard Jendras.
Ukrainians in U.S. Warn: ‘Mr. Putin, Heroes Do Not Die’ Michael Daly March 31, 2014

Historical Examples

Ever on the alert, he regarded himself as the legal protector of the orthodox faith.
Taras Bulba and Other Tales Nikolai Vasilievich Gogol

I can enjoy the orthodox Tory, though I could never understand him.
Alarms and Discursions G. K. Chesterton

Now, I am an orthodox ruin, and the undutiful stepson of a Down East alma mater.
A Modern Instance William Dean Howells

I can also enjoy the orthodox Liberal, though I understand him only too well.
Alarms and Discursions G. K. Chesterton

He had been orthodox, and had exalted childlike peace and faith above doubt and struggle.
Essays on Scandinavian Literature Hjalmar Hjorth Boyesen

adjective
conforming with established or accepted standards, as in religion, behaviour, or attitudes
conforming to the Christian faith as established by the early Church
adjective
of or relating to the Orthodox Church of the East
(sometimes not capital)

of or relating to Orthodox Judaism
(of an individual Jew) strict in the observance of Talmudic law and in personal devotions

adj.

mid-15c., of opinions, faith, from Late Latin orthodoxus, from Greek orthodoxos “having the right opinion,” from orthos “right, true, straight” (see ortho-) + doxa “opinion, praise,” from dokein “to seem,” from PIE root *dek- “to take, accept” (see decent). As the name of the Eastern Church, first recorded in English 1772; in reference to a branch of Judaism, first recorded 1853.