"Can someone explain how a post with a banned word can make it through the filter just fine, but quoting that post triggers it?"
That's because Chess.com either hasn't figured out how to apply the auto filter to the app or they just don't want to. App users are allowed to use banned words and spam more than 6 posts in a row because of this.
It's really sad that if you use the the web site and want to have a conversation about sci-fi author Philip K. Richard (and spell his name correctly) you risk getting a mute.
However it is perfectly acceptable to say:
Go to hell you damn retard douchebag.
Sometime in the last 2 months I got multiple red banner warnings that totally weren't my fault. One of them was for accidentally hitting post before I finished an edit so it was a "duplicate post violation", and the other was 2 or 3 consecutive warnings when I was typing a reply to a post I quoted. I kept editing and editing trying to find what word was triggering it, and it turned out to be in the quote! Nothing I even typed. These should be cleared from my account as it is absurd to have things like that count toward a future mute. I am also tired of having to change Es to 3s and Os to 0s for words that are otherwise benign or are intended for use in a civilized matter. I think I even got a warning once for Google autocorrect changing a word into a different one. Can someone explain how a post with a banned word can make it through the filter just fine, but quoting that post triggers it? Nonsense.