Hmmm?...the first thing that came to my mind was small polyps. Have you passed a lot of them? Are they hard and solid or more like blood clots? Do you have a history of ulcerative colitis or Crohn's disease? Other than the mucoid plaque that you might be passing, have you noticed any black or blood in your feces?
I am not familiar with any parasites
that are blood red, but there may be some.
If you're feeling better I wouldn't worry too much about them, but keep observing and if you keep passing them isolate one of them to give a better description ie. texture, color on the inside, does it 'bleed' on paper, etc.
BTW...they wouldn't be beets, would they?