I've said this a few times, but I often think that the hole they're trying to fill is the one created by the collapse of organised religion.
(Disclaimer: I had a broken night and have had too much coffee already this morning.)
For over a millennium, most people in the western world believed that God created the world, that Jesus was sent to take away the sins of the world and was crucified and then rose from the dead, something about the Holy Spirit, and that there is an afterlife. Another thing Christian doctrine does is place humans above animals in the pecking order, because man was created in God's image. Religion was hugely significant to most people's lives, from a day to day basis with people being baptised, married and buried in their parish, to the whole community turning out every Sunday to worship. At a political level, numerous wars have been fought over religion, including the question of which is the "right" version of Christianity. My own ancestors left their homeland and came to the UK with nothing but the clothes they stood up in because they were persecuted for being the wrong kind of Christians and didn't want to convert to Catholicism. Their cultural identity was so strong that their descendants continued to educate their children in their native language for another 200 years despite the fact that nobody in their family had lived outside of East London for several generations.
Now organised religion has largely collapsed in the western world, or at least its power has been greatly reduced, and left wingers and intellectuals in particular seem to think that belief in a deity is deeply unfashionable and regressive.
BUT, if God does not exist and humans were not created in God's image, where does that leave us? No better than animals, really. We have just evolved, by chance, to create more sophisticated societies than the ones animals have, and it was us, and not God, who decided that we are superior to other species. When we die, that's it, if we are not cremated then our bodies rot away and all that is left is some bones buried in the earth. And during our short time on earth, we have lost that sense of structure and community that came from centering our lives around the church.
The TLDR version is that belief in gender identity theory is largely for people who think they are too clever to believe in God, but cannot accept that their lives have no deeper meaning than those of other animal species. This is why they accept without question that the words "male" and "female" relate strictly to reproductive sex in all other species, but in humans and humans alone these words relate to identity.
What they don't seem to realise is that they have just created a new religion and are trying to force others to adopt it in much the same way that powerful people in all other mainstream religions have tried to force everyone to adopt their belief system since the dawn of time.