When I was hanging out in an Orthodox Jewish community, there was talk about a lawsuit that supposedly had recently happened (it could have been a FOAF story, but bear with me): the sincerity of a woman’s beliefs had come into question in regard to her wearing a hat in a courtroom (she was a recorder), when other people were expected to remove headgear. Supposedly, she usually wore a sheitl (wig), but once in a while, showed up in some other kind of hair covering.
Anyway, she had become frum as an adult, and married a man who was from an Orthodox family, and they were raising their children Orthodox, etc., etc., but someone had evidence that she sometimes spoke on the phone to her mother on Shabbes. That supposedly conflicted with Orthodox standards, and the plaintiff tried to use it as an example of her not being consistent in her beliefs, and therefore, not sincere in them when she was “being Orthodox,” or however you want to term it.
Now, family harmony is a Jewish value, and it’s generally allowed that people who are ba’al t’shuvah (people raised in liberal or non-observant homes, who become Orthodox) can adopt slightly lax standards when dealing with their family of origin: no one is supposed to cut ties with their original family in order to become ba’al t’shuvah.
This woman’s father was ill, and her mother was calling her when she needed to discuss his care with her, and it happened that the time that was convenient for the mother was Saturday. I don’t remember why, it just was. I don’t think it was the only time they talked, but sometimes the mother needed to speak to her on Saturday-- maybe he was in a facility that had offices open on Saturday, but not Sunday. I don’t remember.
But the defendant prevailed.
However, that would be the kind of thing that could be offered as an example of insincerity of beliefs.
I imagine another would be trying to observe more than one religion. If you tell your boss you need Yom Kippur off, then later you say you need time off for Diwali, they are probably going to look at you askance, and don’t be surprised if you get denied.
I have no comment on whether those are either right or wrong. I’m not offering the story because I want to debate it. It’s just an example I happen to know of regarding someone trying to demonstrate to a court that religious beliefs weren’t sincere.