Hey there!
The answer is likely something the lines of disrespect, scorn, or disdain. This line basically means that even if someone doesn't like poetry, they'll still find it to be a medium of genuineness for the writer to express their feelings through. In context, you could replace the word "contempt" with these synonyms and have the line still retain the same meaning.
"...Reading it, however, with a perfect" disdain "for it, one discovers in it after all, a place for the genuine."
Hope this helped you out! :-)
