I'm not sure I can support that, aside from outright scams, I'm stretching my imagination to come up with the scenario you describe. What a person personally believes usually aligns with what they tell their children, because they want their children to share their values and beliefs. This is pretty much a truism, I think, and is not comparable to misunderstanding their religion, so I think you're still conflating the two problems.
That wasn't what I was talking about, but... Really? People being honest about their beliefs to their
kids? Seriously?
We were just talking about Santa, you know? How's that for low hanging fruits of counterexample? It's something parents tell their kids to believe in, although they personally don't.
And then there's the easter bunny, the tooth fairy, Sandman, Jack Frost, and a whole
pantheon for children to believe in. Although their parents don't.
People wanting kids to share their values? People don't even want themselves to share their own values. Most routinely profess to be more acceptable than they actually are, if you give them the slightest hint of what values you want to hear. There's a whole science in the meantime just to pick something resembling the truth from the bullcrap that people will cheerfully tell you about themselves in anonymous surveys.
And for their kids, people at best want their kids to be more like someone better or more successful, and at worst like something that stays out of the way and doesn't need as much attention.
There is a whole body of values people tell their kids, that they mostly don't apply themselves. E.g.,
- you shouldn't just mindlessly follow the crowd (think, "if all your friends jumped off a bridge..."), although mommy and daddy devote hours a day just to being pleasing to one crowd or another. And some would probably actually jump off a bridge if that made them more popular.
- you shouldn't ever tell a lie... although mommy and daddy do. And just flat out lied to you when they professed that value.
- you should take your piano lessons / memorize poetry / whatever extra chore, because it's good for you and you never know when you might need it in the future... and not, say, because mommy and/or daddy like the dose of attention they get when they brag about your results there, while fully knowing that the chance you'll ever need to play the piano in the future is nil.
Etc.
Most stuff people tell their kids is actually not even for the kid's good, as just making him/her something easier to deal with. (From the constant surveillance of Santa, to "if all your friends jumped off a bridge..." and beyond, that's the gist of it.) And in some cases something that mommy and/or daddy can brag about.
If they actually taught you their real values... well, a lot of parent-child talks would be different. And probably horrify most people.
The most common examples that come to mind are a) when two parents with different religions raise children together, in which case they may choose to raise the children according to one belief, but even that doesn't mean deception is SOP. Even if one parent suppresses his beliefs for the sake of stability, it's one of millions of pieces of information parents simplify or withold from children until they're old enough to digest more complexity.
Right, I guess one doesn't believe in Santa, and the other doesn't believe in the Tooth Fairy. Hell of a mixed marriage that. So, I guess, better get the kids to believe in both, just in case
The second example that I am aware of is people misrepresenting their faith in an environment where they will experience persecution. I wish this didn't happen, but I don't think this is evidence of poor character.
People mis-represent their beliefs and values even in a <bleep>ing anonymous survey. That's why there's a whole science in how to phrase it and how to randomize it. People will even profess two mutually incompatible beliefs on two surveys, if they get enough of a hint in the phrasing of what someone would like to hear. Or just because the "yes" choice was about polar opposites.
Seriously, even asking "are you for sending more troops in Afghanistan?" vs "should we pull out the troops in Afghanistan?" yields different results, because people have a tendency to be agreeable and answer "yes". Whatever the question is. That's why you end up randomizing phrases in such polls.
But anyway, if by "persecution", you mean "won't be as popular with Mrs Jones, who actually also fakes being devout to fit in that group", yeah, lots of people seem to be into religion because of that. Or into football, for that matter.