A thought- would it be helpful to allow posters to tick a box labeled something like "Not for Trending or Active" if they want to prevent their post from showing up in these feeds? Sometimes when a sensitive post that has been posted in a specialist area of the site ends up on Trending or Active, it can lead to a really unhelpful influx of people who don't know much about the subject.
I know this used to be a problem when posts from the Black Mumsnetters board ended up on Trending as people would answer without noticing the board it was on- that might have been fixed as I haven't seen but happen for a while.