>androgynous/hermaphroditic
"Symbolism will be [their] downfall" means that [they] use common symbols and code-words that most people would not think twice about because they are so ubiquitous in every day life (Pizza, hot dogs, pasta…etc.) The fact of the symbols existence does not mean that the symbol itself IS evil or that every single person who uses the symbol or code-word is part of the cabal, but [they] can't help but use them in a way that reveals themselves because they use symbols to communicate in a very specific way. (comms to signal allegiance, plans, commands, etc.)
The hermaphroditic occult concepts are very ancient, and the symbols associated with this are equally ancient and widespread.
wizards & warlocks level stuff here, most will only recoil at the sight of a Shiva statue thinking the equivalent of "Shiva man bad", but this is much much bigger than that.