I will not be coming around to the gender critical definition.
I don't expect you to. But this need to preface any reference to a fairly common belief (we can debate the exact extent, but not the truth of that at least) with "gender critical", apparently to reduce it to something rather more "niche" and politicised, does suggest a certain insecurity in your convictions.
Counter to the gender critical belief, I've also heard trans-supportive women state there is no single biologically-based characteristic or experience shared by all women, and as a social class, women share far more experiences within culture.
There will always, always, be exceptions to any view. We have flat-earthers and scientists who are anti-vaxers! That you're aware, on an individual level, of people who "state" this isn't really what's under discussion here, though. The issue's a holistic one: the conflicting rights of two oppressed demographics. I really wish you'd share your views on the universal, to explain more convincingly why you favour the one definition over the other.
For example, I'd argue that that annoying adage "the exception proves the rule" applies here. You say, "there is no single biologically-based characteristic or experience shared by all women". Technically speaking, you could perhaps say that! But the fact is that any 16-year-old girl who hasn't started her periods will be a source of immediate and quite serious medical concern. That individual's existence as an anomalous exception, and the consequent response to her, reinforces the sheer strength of the rule. In contrast, you say that "as a social class, women share far more experiences within culture" - you're suggesting there is some kind of predominant "rule" or pattern here - yet offer no example of this, let alone one that outweighs my biological example above. In fact, I'd argue that the sheer, expansive variety of women's subjective experiences globally and historically, and the impossibility of meaningfully circumscribing this actually disproves the existence of any rule - it makes it impossible to generalise one. I don't know what you'd say because you stay so resolutely away from telling us.
Society hasn't needed to know whether everyone it groups together culturally as women has identical functional biological capabilities, because factually they don't.
One exception to your tendency to avoid the general in favour of the individual is when you can make a safely inarguable statement like this, and I do see it as another form of avoidance. I mean, no one's arguing about "identical. functional. biological. capacities". Our arguments are strong enough that we feel able to be more nuanced in them, as I am above with my acknowledgement of DSDs and anomalies in female menstruation. And as for society "needing to know" this strawman? Well, it's hard not just to type, You don't say! A more honest approach may be to acknowledge that societies have historically "grouped" women because of their common functional biology - their reproductive potential, particularly since the emergence of patrilineal social structures, has presented a risk to the social order unless carefully controlled. This, however, may give the lie to the tomayto/tomahto or chicken-and-egg suggestion that what matters most is social behaviours and perceptions, not biological reality - or, at least, that they matter as much as each other. Because one, regrettably but indisputably, came first.
The likely capacity of pregnancy was assumed of me and the roles of SAHM and eventually working mother were assigned to me.
So, as I say above, what came first? What was/is paramount? A knowledge of female biology was necessary to this assumption. The societal and cultural associations followed.
The social definition of "woman" isn't "my definition" and it doesn't liberate me. I've never claimed that it does. I have no special ability that enables me to escape how society treats women as a class. Women have been culturally manipulated by society for far longer than I've been alive. My transition and inclusion within women didn't divert or change this in any way.
This gets rather abstract again, and honestly returns to some of the techniques I identify above to avoid some very key questions - individual over general, stating the inarguably obvious at the expense of addressing our actual arguments etc.
You and the majority of women experience your female biology as women. I understand that. The first definition of woman references biology for this reason. The word is also used socially, very commonly in other contexts that do not diminish the first definition.
Again, much of this is inarguable, but it does touch on the central issue again. Twenty years ago, all of it may well have been true: I think it would be fairly easy to argue that the casual, courteous use of "woman" and "she" for trans-identifying males didn't "diminish the first definition" back then. But to claim that it still doesn't, in a context of countries - plural - engaging in extensive public debate and actual courtroom battles over these conflicting definitions, is patently absurd. Once again, in evading the issue at hand, you do sometimes give the impression you're not 100% confident in your own convictions.
For what it's worth, I think I've said before but it's maybe time to add again, I do have a lot of sympathy for - and interest in - your position. I would, in the past, have given you "woman" and "she" quite willingly. But now? It's the posts like yours defending why we should continue to make this sacrifice that convince me that we can't afford to. Your arguments just don't seem to address ours - maybe not even to hear them. And how can women possibly hope to be heard better if we give up the only word with which we may distinguish ourselves?