If I understand you, the only recourse open to an objectified woman is to objectify the man.Not necessarily. For instance, in order to accept someone's admiration (which is something most of us would consider a complement), you have to become an object for that person; only insofar as you allow them to ascribe an objective state to you (i.e. the qualities that designate you as admirable) can that person endow you with that honor. If someone on the other hand were to behold you in your pure essence as a "soul," you would escape definition altogether; you would be nothing more than an empty eye, without body or substance. In practice, such a thing can never exist, for we always need a material sign, typically a human body, to alert us to another's presence. If someone were to appear to us as a naked self, we would be totally reified before them, since another person is a perspective on us that thus designates us as a thing, and only to the extent that we, in turn, can designate them as a thing can we preserve our subjectivity before theirs. (This is demonstrated by the fact that when you objectify a person who stands in your presence, suddenly your awareness of yourself before them--in other words, your existence as a thing in the world--all but vanishes.)
All of this is to say that the thing you criticize the MBTI for is not only intrinsic to human interaction but something that many of us strive for in one form or another (the only alternative to at least accepting your condition as a thing is to wish for the death of other people).
You yourself are no exception to this rule. Since you clearly don't wish to kill us all, everything you do on this website is a kind of act, a role that you've taken on and come to wear like a costume with nothing underneath it.
This is plainly objectionable.