Huge respect to you Miranda; you’ve been actively involved in this way longer than I have and it's entirely possible that a) I’m being naïve and/or b) I'll end up feeling as you do about the TS Voices statement but...
Writing for public consumption is difficult at the best of times. Writing when people on all sides (and none) are ever ready to go on the attack and when you have skin in the game is almost impossible. Something is omitted that one reader thinks is essential, something is included that another considers an appalling distraction, words become 'literal violence', grammatical errors are proof of stupidity, whataboutery responses suffocate the central argument and distort the original intention. And we are all left more angry, more distressed, and less able to acknowledge each other’s vantage point or simple humanity.
If the TSV statement is read for what it actually does say, and with a presumption of integrity, I think that the OP is entitled to her sense of hope. The group explicitly acknowledge that ‘safety would be compromised’ by self-ID and by men’s ‘demands of access to female only spaces, their frequently demonstrated express misogyny, disrespect for the biological needs and specific rights of young girls, mothers, lesbians and many other, traditionally, female only, social groups.’ They also differentiate between ‘women’ and ‘transsexuals’ and state their objection to ‘any “trans rights” encroaching and gradually erasing women’s rights’. Of course the statement is written from a transsexual vantage point and mostly deals with their concerns. That is entirely legitimate; they, as we, are threatened by trans ideology. But there is an explicit intent to hear and understand women’s concerns and to find common ground.
Their statement has lifted me.
My hope is that, rather than dismissing them as ‘just silly’, ‘whining’ or ‘ridiculous’ we might start with an assumption of sincerity and an acceptance that there is indeed a common enemy and we are stronger together.