"a rigid adherence" is correct and can be used in written English.
You can use it when you want to emphasize that someone is adhering strictly and consistently to a rule or standard. For example, "The coach demanded a rigid adherence to the team's practice schedule."
When the show was relaunched in November 2003 it departed from a rigid adherence to the singles chart for the first time.
This normally includes a rough adherence to some proximity of the truth and a rigid adherence to the agreed-upon message of the day.
Most have by now picked up the stylised fact that a rigid adherence to the gold standard made a bad slump worse.
It switched from BBC1 to BBC2 last year after the latest high-profile relaunch in 2003, which moved away from a rigid adherence to the top 40 format for the first time, failed to boost ratings.
Here in the homeland of schadenfreude, the zeal for unmasking academic frauds also reflects certain Teutonic traits, including a rigid adherence to principle and a know-it-all streak.
Domestic carrier IndiGo is a success, Reuters says, in part because of a "rigid adherence to a disciplined business plan, a task that grows more complex as the airline, which now has 50 planes, adds a new aircraft every month".
But this is a case where rigid adherence to a rule ("make sure to add 'alleged'") is no substitute for careful thought.
Kant's conception of morality as a matter of rigid adherence to strict principles emerges as partly an intended remedy for his own hypochondria.
Given the prevalent view that illnesses have a spiritual origin, rather than an infectious one, we speculate that rigid adherence is a goal of health care workers more often than patients [ 48].
The principle against a public authority fettering its discretion by rigid adherence to a policy also applies to the exercise of discretionary police powers, as indicated by obiter dicta in the High Court case of Chee Soon Juan v. Public Prosecutor (2011).
He had acted as a staunch defender of Puritan orthodoxy, with its zealous advocacy of a "pure," unaffected form of religious worship, its rigid adherence to a simple, almost severe, mode of life, and its conviction of the "natural depravity" of "fallen" man.
