I do actually. I care because I think language matters, it affects the way we think, and the way others think about us, it affects our emotions, as women it affects our standing in society.
If you look at the history of repressive regimes one of the first things they do is immediately seize control of language media , newspapers, radio, tv etc . They control the information that goes out, they monitor the language that is used, and in many cases they change the language that is used to describe both current and historical events. Especial care is given when describing those who oppose repressive regimes. People who fail to respond to the new use of language are vilified, their motivations are seen as suspect, others are encouraged to isolate them, shame them and report them.
Now, I am not for a moment suggesting that the T movement is as repressive as say, the Taliban, Putin, or Mao’s China in the cultural revolution, but some of the methodology it employs is surprisingly similar, in terms of how it has weaponised media outlets both print and online, the response to criticism, how shame and isolation is used to silence opposing voices, how individuals who speak out are threatened and bullied.
So yes, things as small as objecting to the word cis, or not getting caught up in pronoun angst are greater than they seem, because they represent a pushback . Pushbacks fail when there is only one person pushing, but effective when there is a crowd of pushers . It’s not about transphobia, it’s about not being railroaded into a way of thinking by a very vocal minority who have adopted clever tactics which for a time blindsighted a lot of us.