Yeah there's actually been interesting stuff around this lately because people have claimed to have sincerely held religious beliefs re: mandatory COVID-19 vaccination exceptions. In cases like that the definitions of "sincerely held" are very relevant and questioned by the court.

Here's some case law where a court found a plaintiff did not hold a religious belief sincerely. I pasted the relevant section here, states actually have definitions around what constitutes religious creeds/religion/sincerely held belief. If you Google these phrases with "case law" you'll find much examples.

The administrative agency charged with enforcing the FEHA, the Fair Employment and Housing Commission, has also enacted a regulation defining “religious creed.” California Code of Regulations, title 2, section 7293.1 (regulation 7293.1), defines “religious creed” as follows:  “ ‘Religious creed’ includes any traditionally recognized religion as well as beliefs, observations, or practices which an individual sincerely holds and which occupy in his or her life a place of importance parallel to that of traditionally recognized religions.” Consistent  with regulation 7293.1, plaintiff argues that his commitment to a vegan lifestyle occupies a place in his life parallel to that of traditionally recognized religions. Regulation 7293.1, by its express terms, reflects the notion that religious creed extends beyond traditionally recognized religions to encompass beliefs, observations, or practices occupying a parallel place of importance “to that of traditionally recognized religions” in an individual's life. As will be discussed later, that concept of religion originates from two United States Supreme Court cases involving conscientious objection to military service-United States v. Seeger (1965) 380 U.S. 163, 164-188, 85 S.Ct. 850, 13 L.Ed.2d 733, and Welsh v. United States (1970) 398 U.S. 333, 335-344, 90 S.Ct. 1792, 26 L.Ed.2d 308.

Some more reading:

https://www.callaborlaw.com/entry/defining-sincerely-held-religious-beliefs-that-might-excuse-mandatory-covid-19-vaccination

https://www.eeoc.gov/laws/guidance/section-12-religious-discrimination#h_9546543277761610748655186

https://www.sfchronicle.com/sf/article/Nearly-200-S-F-police-staff-want-religious-16486136.php

https://casetext.com/case/malnak-v-yogi (long but gets in to all kinds of religious tests applied by court system and the corresponding law)