I can only answer with an example from within my own family.
My sibling's partner has suffered long and deep hurt from the refusal of his birth family to refer to him as 'he/him' after his transition. They go out of their way to refer to him as 'Chris' (or rather his own gender-neutral birth name), or 'my child Chris' or 'my sibling Chris' or 'they'. By doing so they are denying his gender-identity, and doing so deliberately (and passive-aggressively) -- malicious compliance, it has been called elsewhere.
Imagine then the pain that he would be reminded of, if somebody in this venue insisted on avoiding pronouns unnaturally.
It is possible to learn to use somebody's chosen pronouns when you've been made aware of them -- or to default to natural sounding neutral language when you don't know/are not sure. Some of us have been doing so for over 40 years in all walks of our lives.
And if somebody's chosen pronoun contradicts your deeply-held beliefs, or you find you really can't adapt your writing style, it's possible not to engage, or to withdraw gracefully from a conversation online. (Face-to-face is different).
Edit: this is longer than my original response, so I want to emphasise that I TOTALLY AGREE with the CoC change (while believing that its introduction has been a failure on all levels).
Also, I expect downvotes, but I'm staying true to myself. As everybody should.
By discussion/reading, I have come belatedly to understand that for some people, it is not a matter of adapting their writing style or disengaging/withdrawing; the change in the CoC fundamentally challenges their deeply-help beliefs and they can't see any way of continuing to participate while staying true to their beliefs. This does not automatically make them 'bad people' (unless and until they demonstrate unmistakeable intent to hurt people, including denying their existence, having been informed what can be included under that umbrella that they may not previously have realised). We should not shun and excoriate people on the basis of their beliefs -- actions/speech (or patterns of actions/speech) is what matters here (and -- more practically -- what is actionable). And a single action isn't grounds for launching a nuclear attack.
I apologise unreservedly for not understanding before why people might find the CoC changes impossible to accept -- when you've never experienced something, it's hard to recognise how it impacts somebody else but that's no excuse for not apologising when you recognise you've been wrong. So, again, I apologise to those who are finding this hard for reasons of belief (while wholeheartedly refuting the argument that belief is an excuse for hurting people).
I may disagree with underlying beliefs, but it can't be gainsayed that some groups are feeling pain because of this change, while others believe it improves matters. I have no sympathy for those who are being denied a route to be deliberately hateful, but I do understand the pain of those who would choose to 'live and let live' and have not previously understood how that can transmute into 'keep quiet, don't rock the boat, don't tell us who you are and you'll be fine'. I DO NOT accept that position -- it favours the people who don't want to know, above the people who are expected to keep quiet. I do understand that the people who are required to accommodate the change might find it impossible to adapt.
I have an analogy that has helped me to realise where some people are coming from.
I have spent my entire life not accepting the usage of 'he' in English as the generic/gender-neutral third-person pronoun -- I was taught by my mother and also at (an all-girls) school that it was wrong, and belittled women, who were the equal to men in all fields (but not their equivalent).
I spent my University years and my years in employment fighting the usage, and am pleased that it is no longer -- in some quarters at least -- the default generic pronoun; and that correcting the usage of 'he' to 'they' in some venues is no longer challenged. There are places it isn't recognised, or is actively ridiculed, and those are places I do my best to avoid, because I can't participate and still stay true to what I believe on the subject.
Let us suppose that the CoC had been modified to mandate the use of 'he' as that generic third-person pronoun. Let us also suppose that the reasoning has been explained and it explains the 'benefits' (however 'benefits' are defined) to a group of people not including me who feel disadvantaged without the change.
As a one-time professional writer, and a sometimes teacher of writing, I'm confident that I could adjust my writing style to avoid using it at all; or I could modify my behaviour not to get into situations where it might be necessary; or both.
But -- and this was my visceral reaction when I thought about it for a few moments -- I could but would I? Doing so requires me (1) to give up 6+ decades of believing otherwise, and (2) give the appearance of condoning the change -- disregarding completely something I believe fundamentally.
My options would all be painful... Swallow my principles? I couldn't do that. Argue against it? I suspect it would be futile, and anyway I might agree reluctantly that it's an improvement for the group it's intended to benefit, and no worse for most people.Decline to participate any more? I would miss SE enormously as a resource, although I've never bought into the idea of it as a 'community'.
Perhaps at best it's a set of distinct communities, with a few points of overlap, but there are places within it where -- even if I lurk, or spend hours researching similar questions and/or crafting questions that won't get closed immediately, I feel that at best I am tolerated, and will never 'belong'; and other places I would never venture because they're toxic, or not relevant to my interests). I suppose I could still lurk, and look for 'community' elsewhere.
I'm fortunate -- the tides of change are not moving in a direction contrary to my beliefs, but I don't envy anyone who finds themself swimming against the tide. (Some of them -- good riddance. But many would be a real loss).
I do believe that the change to the CoC addresses a real issue for a group of people who participate here; and I also understand that it causes a real issue for some other groups.
I regret to say, I don't think there's a solution that doesn't involve pain for some people. If we return to the previous state of affairs, we will hurt those whose presence has been (to be blunt) tolerated on the condition that they keep quiet about who they are and don't make others uncomfortable, otherwise they're expected/driven to go elsewhere -- is that an equitable solution?
If we adopt the new CoC, different groups of people may have to keep quiet about who they are or leave -- is that equitable?
Is it possible to weigh the competing needs of two groups with very differing beliefs and come up with a solution that suits everyone? No, it isn't -- this isn't Physics (my degree subject) or IT (my career) where you can do the work and demonstrate what fits the theory/meets the spec and what is clearly wrong. It's people and beliefs and messy as all-get-out and I don't have a solution.
It will come as no surprise that on balance I favour the CoC change (if I were in position to do so, I would reword the FAQ, and I would definitely handle the whole sorry roll-out differently) but I will no longer dismiss the impact on others as trivial. Which is, I acknowledge, no consolation to those faced with painful decisions.