It appears that you've just passed the infamous mucoid plaque; this is not a parasite, but simply impact fecal matter that it has been accumulating inside your intestines; this plaque covers your intestines walls and takes the shape of its inside like a mold, hence the disk looking things.
It does not disintrigate like typical feces and its very rubbery in nature and this plaque prevents your body from fully absorbing nutrients and can harbor parasites and plenty of toxins.
Youre most likely passing mucoid plaque (which can be a few feet long) due to your fiber regime, as the fiber slowly binds and drags it out.