I wonder whether the pronoun ITS is ok here, or THEIR would be better, since the"former group" refers back to the 'traditional views', including many views:
I argue that neither the traditional views of metonymy nor contemporary theories could be considered genuine frameworks to explain ALL metonymy. For the purposes of this study, my main criticisms against the former group concern its/their? inability to differentiate ...
For the purposes of this study, my main criticisms against the traditional views concern their inability to differentiate ...
You'd lose more points for being too obscure than for repeating. Markers don't like to have to keep looking back and guessing.
Also, you might consider using all instead of ALL. Italics (or underlining if you don't have italics), not capitals, has always been the way to express emphasis.