Do you eat a lot of celery or raw vegetables? We can't digest cellulose (the stringy pieces in celery) and so that will come through your system with almost no change in structure.
If not, a stool sample is definetly needed to check the content.
I mean its look like a mesh or net. exactly like you mentioned parasites (like tapeworm
what do you mean about "look like a fungus"? Yeast are tiny tiny individual cells, you would never be able to see them in your stool (unless you are looking at a sample under the microscope and even then I'm not sure if yeast would be found in stool).
There are parasites (like tapeworm) that you may be able to see in your stool but it is more likely just food that wasn't digested. Ever looked after you ate corn? Yuck, half of the corn looks the same way you eat it.