How open-minded am I - I'm unsure.
To me, being 'open-minded' intones the capacity to listen to the opposition's cogent, civil, and coherent viewpoints and arguments, and upon hearing such arguments, be able to make a rational, thought-out decision and action upon such argument (free of anger, fear, emotion, or euphoria).
Open-mindedness is a two-way street - just as members in our community argue and advocate for certain laws, rights, and societal acceptances, obviously, those on the 'other side' will also have their own viewpoints RE: why our community is in the wrong. Reasoned discourse between both sides is necessary, without negative name-flinging, anger, or devolvement into childish, boorish arguments and behavior. One cannot consider oneself 'open-minded' if one is merely angry and boorish when one doesn't get one's way.
As this online forum declares - "We stand at the crossroads of gender balanced on the sharp edge of a knife." This is a difficult journey for many, with the potential for a precipitous fall; we must walk this journey fully cognizant of ALL viewpoints on the matter of transgenderism, and be able to accept - or decline - through reason and intellect, such viewpoints with maturity and civility. That (to me) would be open-mindedness. [This concept applies to issues other than LGBT issues, as well]