Interesting post, Spooky. I am going to try and reply to the points you make, in good faith of course!
First of all, thank you for admitting that you don't always fact check sources you rely on if they support your existing point of view. I think this is something we are all guilty of but it takes a certain amount of honesty to admit it.
When you mentioned having to explain to people what gender identity means, and the idea that it might be a new concept for some people on this board, I can assure you that it is not in any way a new concept to people on this board. If people are asking you to explain it, it's not because they have never heard of this newfangled thing called gender identity, it's because they've heard all about it, think it is all a load of nonsense, and want you to explain it because they don't think you will be able to explain it without it becoming obvious that it is all a load of nonsense. Perhaps you would see this as not arguing in good faith!
I think drawing a parallel with religion is actually very useful, although I appreciate that some people who believe in gender identity object to that comparison.
Put it this way: there are a great many people in the world who are Christians. They believe in God, the Father, Son and Holy Spirit, they believe that Jesus was the son of God who came to earth to save us from our sins and offer us a path to salvation, they believe that he was crucified, died and was buried, and that three days later he rose from the dead and then ascended to heaven. I personally do not believe any of these things, but I believe that Christians exist and I can explain more or less what it is that Christians believe. If I wanted to argue with a Christian, or embarrass a Christian, or perhaps object to Christian beliefs forming the basis of laws which apply to non-Christians, I might ask them to explain what it is they believe and why. I would not expect them to renounce their faith on the basis of a conversation with me but I might succeed in getting them to admit that there is actually no proof of what they believe - that is why they call it "the mystery of faith" - and that their choice to believe in it should be a free choice and not imposed on the rest of us.
For what it's worth, I think Christians are actually more coherent in what they believe than those who believe in gender identity. Certainly, I have a fairly clear idea in my head about what God the Father is supposed to be, an even clearer idea about Jesus, i.e. God the Son, and when it comes to the Holy Spirit, well, I guess we're back to some sort of intangible "God essence". But since the laws of this country aren't being made according to Christian beliefs, and since you can no longer be punished for not being a Christian, or not being the right kind of Christian, I don't think it greatly matters. Let them believe what they want to believe. I will only object if I think people are being harmed.
I accept that trans people exist, the same way that Christians exist. And I accept that for those people, their gender identity may be very real to them, the same way God is very real to Christians. But just because something is real to them does not mean it is actually real, or real to everyone. Christians believe that God is actually real, whether other people believe in it or not. Atheists believe that God is not actually real, whether other people believe in it or not. Agnostics believe that God might be real, but haven't seen any compelling evidence to convince them either way. And perhaps some people believe that God is literally real to those who believe, and literally not real to those who don't believe.
As you can see, it is very personal.
For people who are strong believers in gender identity, it is very important to promote the world view that not only is it real, but that everyone has one. Those of us who maintain that we do not have or believe in gender identity are repeatedly told that we are "cis", and that not believing in gender identity is an example of "cis privilege", i.e. we are so used to being the privileged majority in this world view that we don't even realise how privileged we are. This is particularly hard to stomach when, for example, it is implied that a woman of colour who has escaped a sexually abusive relationship and is seeking counselling is more privileged than a white, male-born person who identifies as a woman and she should therefore "be kind" and not object to sharing a single sex space with such a person.
It's also difficult to stomach when the people who believe in gender identity insist that it exists and that everyone has one, but cannot explain in clear terms what it actually is or why they are so sure that everyone has one.
What are the elements of "womanhood" which aren't related to having female reproductive anatomy? What is it? Is it about wearing dresses? Makeup? Liking the colour pink? Playing with Barbies as a child? Enjoying shopping as a leisure activity? These are stereotypes. There are men who do these things and women who do not. Defining a woman as someone who does these things excludes huge numbers of women who do not do these things.
Believers in gender identity claim that it is not about these things, but they cannot explain what it IS about. What are the features of the identity that "matches" having a vagina, so that if you have these features but were born with a penis, you know you were supposed to be born female and something went wrong somewhere? Nobody can explain.
Some people say that identifying as a woman just means whatever the individual wants it to mean. So for some people it might mean being biologically female, i.e. the sex class with the potential to get pregnant and give birth, and for some people it might mean liking the colour pink.
This is a more honest answer.
But it creates a problem: if what makes someone a woman is different for everyone, the group of people you are calling "women" have absolutely nothing in common with each other. If the word "woman" means whatever the individual wants it to mean, it doesn't actually mean anything. And that means we don't need a word for this group of people, and they don't need their own toilets, prisons or sporting categories. It makes it very difficult to justify having women only spaces at all, let alone trans women being allowed to use them on the basis that they are the same as women.
So this is why those who believe in gender identity continue to insist that it not only exists but that everyone has one, and that women and trans women have the same one which is why we should be using the same toilets and competing in the same sports, even when many of us disagree completely.