So I read 'identifying with character X' as understanding him/her as a subject as opposed to (or as well as?) an object.

I read Cesperanza's 'identifying with character X' as choosing a character for fanactivity because of their canonical or presumed similarities to the fan doing the choosing. So, to me, objectify vs. identify works out as something like, 'pick characters because of what I'd like to do to them' as opposed to 'pick characters because of what I'd like to do.'

And I agree with hth's position on how and why it's problematic to posit 'identify' with as the heart of fannish activity.