What is the test for determining the sincerity or authenticity of a person's religious beliefs?

Under special circumstances, the First Amendment seems to tolerate an inquiry into the sincerity or authenticity of an individual's professed religious beliefs. See U.S. v. Ballard, 322 U.S. 78, 64 S.Ct. 882, 88 L.Ed. 1148 (1944) (inquiry into the petitioners' belief in the facts they asserted as religious truths was appropriate in a trial for mail fraud); Witmer v. U.S., 348 U.S. 375, 381, 75 S.Ct. 392, 395-396, 99 L.Ed. 428 (1955) (sincerity of a registrant in objecting, on religious grounds, to participation in war was necessary factor in determining conscientious objector status). ¹ Although these cases superficially appear to authorize government scrutiny of the strength of religious convictions, the cases themselves do not make such an inquiry.