... I think her blog entry focuses on the negative without acknowledging that many of us do find empathic support from cis people, just as many, even most, people wear masks, keep their distance and respect closures.
I don't think she meant that nobody supports us. I believe that the goal of her blog was to increase acceptance of trans people by presenting the people who don't accept us with evidence that they are wrong. That is, that the cis people who buy into the transphobic slanders simply need to be educated.
The "hard lesson" that she speaks of is that most people who hold unreasonable beliefs aren't going to have their minds changed by evidence or logical argument. If a huge fraction of the USA population (and maybe elsewhere, too) insists on holding onto an irrational belief even when doing so kills them, there isn't much hope of getting them to let go of their transphobia (which doesn't harm them) simply by educating them.
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What seems likely to change attitudes most is simply cis people knowing trans people personally. I recall that what really changed public attitudes towards gay people (esp. gay men) was when so many gay men came out of the closet, in reaction to the AIDS epidemic. I was constantly reading about families which initially had negative opinions of gay men (and/or lesbians) as long as they didn't know any personally, but turned around when a beloved member of the family came out as gay (especially if said family member was dying at the time.)