To me, the deadlock seems to come down to a fundamental disagreement on basic assumptions and a disagreement between who is and is not a legitimate stake holder in these conflicts.
Do you consider females to be legitimate stakeholders?
For the trans inclusionists, trans identity is treated as an immutable characteristic of the human experience, and like other similar characteristics (race, sex, sexual orientation, etc) should not be grounds for discrimination. Indeed, often trans identity is seen as a derivative of sex identity, though I'm not convinced this is a useful framing beyond being used a legal tactic and the existing nondiscrimination law.
For liberal trans exclusionists, trans identity is seen as little more than a delusion that, as a matter of politeness, should be accommodated when possible within the limitation that it does not interfere with the other, real interests of protected class characteristics.
You're black-and-whiting this. Let me try once again to provide a more accurate representation of a perspective.
"Identity" as a whole is not immutable. In all aspects of human development, identity is a changing element of our personality. It's also not something that is determined solely by one's own belief about oneself. Identity resides in the intersection of how one views oneself, how other people view one, and objective reality.
As an example, consider that I mentally view myself as tall. Other people may or may not perceive me as tall, depending on their starting point. Put me in a room of professional NBA players, and I suspect they will universally view me as short. Put me in a room of people with dwarfism, and they may very well agree with my assessment of myself that I am tall. Unfortunately, if you actually measure my height relative to the distribution of heights for adult humans... I am
indisputably short. There is no question, no argument that can change that fact. Even though my mental map of myself with respect to the world around me thinks that I am somewhere around 5'7"... In reality, I am 5"2. My brain is wrong. My identity as a tall person is at odds with the height class for which other people on average would identify me, and is absolutely incongruent with the objective fact of my height.
The conflict is similar when it comes to transgender issues. Their perception of themselves, their personal internal identity, is very often at odds with how other people would identify them, and is completely incongruent with the objective fact of their sex. There is a fair bit of wiggle room in there. Consider that both Blair White and Alex Drummond perceive themselves to be 'women', and both identify as women. But if you put them in front of an unbiased audience with no prior knowledge of either of them, those other people would very likely identify Blair White as female and Alex Drummond as male. Objectively, they are both indisputably male. White is highly likely to be perceived as female by unbiased observers, and therefore it is far more likely that their claimed identity as a 'woman' will be unchallenged. The same does not hold true for Drummond.
I think it's worth noting that transsexuals have been around for a long time. They are not common, but they're not at all unheard of. But up until recently, those transsexuals had been treated clinically, had a diagnosis of gender dysphoria that was significant enough to necessity physical transition, and they put significant effort into successfully passing as the opposite sex.
And with very, very few exceptions, they have been accepted as the sex they have transitioned to in nearly all cases. The conflict has arisen as a result of the activist push to make gender identity a matter of declaration and nothing more... and to require that everyone else recognize and affirm that declared identity.
The problem isn't transgender people or their existence. The problem is self-declaration, the obligation for everyone to accept that declaration without challenge, and the insistence that an entire sex class be defined NOT by the members of that class but by those who wish to be viewed as that class.
The problem is that this self-declaration being treated as absolute unassailable truth erodes the rights and safety of females as well as homosexuals.
Doesn't it bother you even a little bit that we've come full circle, back to a point where homosexuals are being demonized and harassed because they don't engage in heterosexual sex, and don't consider members of the opposite sex as potential romantic partners?
Doesn't it bother you even a little bit that we've come full circle back to a point where females are being derided and threatened with violence for speaking up in defense of our own safety, dignity, and rights?
When it comes to an issue like sports, it's a matter of whether you see it as a complicated conflict between equal stake holders in which an equitable solution must be reached vs those that see it as unreasonable people making unreasonable demands that should be ignored.
It's the difference between sports leagues who are setting rules about hormone levels and whatnot as a reasonable compromise and those that feel any accommodation for trans people is letting delusional people take up too much priority.
Who do you see taking the latter position? Do you have some evidence for the position that you believe you are arguing against?
The kneejerk response to maintain the status quo, despite it being obviously bad for trans people, shows that there is little interest by some to treat the grievances of trans people as legitimate.
It's not a knee-jerk reaction when the "progressive" platform is bad for females and bad for homosexuals. And in a great many cases, it's not obvious that it's bad for trans people either. It's not bad for trans people to have access to a separate locker room or prison wing. It's not bad for trans people to have access to trans-specific refuges and shelters.