It is neither cancerous nor a pre-cancerous condition. I finally had a chance to look this one up: Pathology labs use stains on tissue samples. Eosinophilic refers to tissue that becomes stained pink or red as the tissue absorbs more of that particular type of stain (eosin.) Metaplasia, as already explained is a change in the cells, which results from chronic infections or inflammations. Most importantly, metaplasic cells changes are not an indication of carcinogenesis.
My mom had pre-cancerous cells in her uterus. She had a hysterecomy. She never said what the technical name was just that it was in the last stage. And being that it was almost twenty years ago I doubt she remembers.
I am not certain it is either of those choices. Eosinophils are a type of leukocyte, a part of the immune system. As for "Metaplasia"... I cannot state that I have ever seen the term, but wouldn't that mean some sort of not-particularly-alive collection of cells? Like a growth, perhaps. I am just guessing here, but perhaps you have a condition that your body is interpreting as an infection or inflammation, and your immune system is fighting it.
I just don't know. I would love to know the real answers to your questions when you learn them, so please share!
What does your doctor say? If you have the results, you should have had some sort of conversation with the doctor.