It seems quite clear to me that the "neither view", wherin a neutral entity is one that is neither mental or physical, is a form of metaphysical realism. But it gets confusing, and perhaps downright impossible to make sense of, an entity which is BOTH mental and physical. To make matters even more confusing, in neutral monism there seem to be certain cases where the "subjective" and "objective" "become the identity realtion,"(1) that is, become the same thing only seen from different perspectives.
This "neutral realism/new realism," as I have heard it called... is it a form of metaphysical realism? Or does it deserve some different designation?
--Take "realism" (fundamentality of objectivity) here to be understood as the negation of "idealism" (fundamentality of subjectivity) as understood by someone like Berkeley
--(1) "become the identity relation" taken from SEP on neutral monism