I am a trans woman. I am full of admiration for Zooey Zephyr, for the dignity and resolve she has exhibited as this incident has progressed.
It light of your comments, it is interesting to note that, once the conflict materialized, some of her opponents on the floor of the House began purposely misgendering her.
The kind of smugness and glee you described on the faces of the women in the corridor is the kind of thing seen more in groups than in individuals -- as though groups give them courage to be open about how they feel. But I don't think this is primarily about hate; I think it's about fear.
Cis people cannot relate to the trans experience. There is no cognate in their world to the experience of feeling wrong in your own skin; and people tend to fear what they can't understand. It's not a white reaction; it's been a piece of the fabric of being human since time immemorial: "Stranger is Danger."
The real question in these matters is how to respond to this kind of aggression; and in this vein I think the words of Howard Roark, the hero of Ayn Rand's novel, "The Fountainhead," are salient. Ellsworth Toohey is a popular columnist with immense power in the city of New York, and he has orchestrated a merciless and effective campaign to deny Roark, a brilliant architect, from getting work. He has done this to destroy him, because of what Roark stands for. They run into each other one night on a bridge.
Toohey: "There's the building that should have been yours. There are buildings going up all over the city which are great chances refused and given to incompetent fools. You're walking the streets while they're doing the work that you love but cannot obtain. This city is closed to you. It is I who have done it! Don't you want to know my motive?"
Roark: "No!"
Toohey: "I'm fighting you and shall fight you in every way I can."
Roark: "You're free to do what you please."
Toohey: "Mr. Roark, we're alone here. Why don't you tell me what you think of me in any words you wish."
Roark : "But I don't think of you."
That's the spirit. There is a principle in martial arts to the effect that you don't fight your opponent, because fighting gives him power. There's a lot of truth there. Evil wins when we give it respect, when we elevate it with fear. This we must not do.
This doesn't mean submission or compliance with evil. It means you treat it as unimportant and act as though it doesn't matter -- because it doesn't. Gandhi understood this. And, as Gandhi's experience demonstrates, it's not a safe course of action. But it's the right course of action. Any other merely gives evil more power.