you wrote:
Perhaps a better way to phrase it that is consistent with your concern would be to say, "The members of one religion invariably state a falsehood when addressing the essential elements of the other religion."

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I like that phrasing better, but still it presupposes that one group knows they are correct, and knows the other is incorrect when they both feel they are correct. How do you "know" which is a "falsehood"?

I would prefer to do away with the entire notion of lying or truth-telling, correct or incorrect, truth or falsehood, (all subjective), and instead focus on pure logic. Then it would go something like "The members of one religion always apply logic correctly, while the other group always disregards logic".

JMHO,
morris