This is well argued.
The first thing is that the very nature of politics is that it views other humans as collective demographics - a gender group, an orientation, ethnicities, nationalities, religions, etc. - rather than as individuals. There's nothing wrong with having a political opinion, but interacting with a real human while carrying the charge of a perspective that dehumanises their individuality, things can get very toxic, very fast.
There was a purported Joseph Stalin quote along the lines of, "The death of one man is a tragedy, the death of a million is a statistic." Combined with all the genocides and hate crimes throughout history, it's easy to see why we are better off connecting to individual fellow humans directly, rather than through the lens of political battlegrounds regarding their demographic.
Secondly, it can be useful to speculate on the real motivation behind transphobic commentary. I see a few possible types.
Many disenfranchised men would have been given vast privileges in pre-
Sexual Revolution era. Each was entitled to a submissive wife, a vibrant career and disproportionate wealth and authority in society. By contrast, many such men today are left to rot in isolation as if these individuals deserve punishment to compensate for the excesses of their antecedents. The grievances of low-status males are valid in their own right, but responding to them without attacking all progress made in rights for women, minorities and the LGBTQ community is a challenge.
The most putrid dungeons of the internet have given rise to various victimhood cults which channel the rage of these men into the narrative that they are denied 'free speech' for wanting to unload their veiled contempt towards various formerly-submissive minorities, along with the associated half-hearted intellectualism of their groupthink.
Meanwhile, religious people often have strong views about human sexuality and seek to enforce it on others, again railing against anything that does not fit their simple narrative of straight, cisgender roleplaying. Rather than science, this is based on religions seeking to control people. They strive to increase their political power by encouraging procreation amongst their people, in combination with brainwashing children to follow suit.
And finally, some women have a negative view of men (understandably, given what many have been through). Their own sense of identity - be it solidarity with other women, victimhood echo chambers or a sense of superiority - is threatened by the prospect of a MtF transition, again provoking an aggressive reaction.
When all is said and done, the simple solution is to make the effort to view fellow forum members as human first, and objects of politics second. If the temptation is to respond with political commentary when an individual is in distress, that's a good sign that it's time to stop.