I think something to consider is that a lot of people will believe there isn't a notion of gender separate from sex.
For me, and I assume others including some members of trans communities, Gender is more an identity.
This has always been slightly the case when we would call more masculine girls 'tomboys' (which, interestingly I think used to mean naughty boys but now we use to mean less feminine girls)
You can be scientifically a sex, no one can argue what that sex is, and I don't really see how you could fully change that, even with hormones and surgery etc.
But gender; if gender is an identity, how you feel and behave and who you believe you are, that can be separate from sex.
As a society we have constructed gender norms and we all play in to them in one way or another, so if someone strongly doesn't feel that fits them and the opposite gender norms apply to them and makes them feel truly themselves why does that affect anyone else? (I understand that there are potential risk in criminal situations, but plenty on non trans people commit crimes and just as with race and other protected characteristics we can't make the rules for a whole group based on just the awful ones within it)
I'm not saying there aren't areas of the trans gender discussion that don't need to be looked at in greater detail, I just don't agree with dismissing it as playing dress up as a solution. (I'm not saying that's what you or anyone else is doing so please do not take offense)
I do, as stated, understand that with prison, hospital sports and other aspects we can't ignore biological differences and need to keep everyone safe, but that does extend to everyone. Not just people who identify as their sex assigned at birth, and not just members of the trans community.
If someone else feels like they are a woman, and truly lives that way and it harms them to pretend otherwise - it does not affect my identity as a woman, so I have no problem calling them 'her', inviting them to girls nights, hen dos, standing next to them at the hand dryer in the ladies bathroom, pretending I'm meeting up with them if they're getting unwanted male attention in a bar or club - just like I would any other woman.
Equally, if I didn't believe in the notion of marriage and a friend got married and took their husbands name, I wouldn't refuse to call them by their married name just because I don't believe in things.
So if for you, gender is synonymous, or inextricably linked to sex - then we do just hold different opinions and can both be a little bit wrong and/or a little bit right. Which is of course fine, I truly think the main issue comes from assuming one side is entirely right. Or assuming that we all need to agree, as long as everyone can live their lives safely - trans gender or not - then surely it doesn't matter? (of course, that's very idealistic, but hey, a gal can dream)
I also try to be really careful and open minded when I discuss things with my kids, because for all I know they could come to me one day and say 'I am (trans, religious, gay, don't want kids, non binary etc)' and I wouldn't want them worrying what I might say, or hiding it or dealing with it a lone because they were worried I wouldn't accept them. I am not saying anything about anyone on this thread, we all parent differently and think we're doing the best thing for our kids, that's just how I feel I can do right by mine.