The right-wingers love to get hold of the concept of "gender whisperers" and bandy the term around without understanding something. You cannot make a cisgender male child think he's a female or vice versa. What those more willing to accept reality know is that they are saying, "If you are not cisgender, it's okay to embrace that.
In Alan Turing's case, he was a cisgender male who was sexually attracted to other males and estrogen therapy was the wrong course for him.
Germaine Greer's theory, however, is akin to saying that a fourth generation Chinese-Australian is not an Australian, as the default description of an Australian is a tall, blonde haired person wearing a t-shirt, shorts and thongs with a suntan. A fourth generation Chinese-Australian may say, "My ancestors were Chinese and they married within the Chinese community, but I don't speak a Chinese dialect and I've never even been to China." Just like a fourth generation Anglo-Australian might say that yes, they speak English but they've never been to Britain.
How I best describe transgenderism, but some don't see the connection, is this. The year is 1988, and a 19 year old has worked hard for three years, two part-time and one full-time, to buy a secondhand XC Falcon. The XC Falcon has an AM Radio and the 19 year old wants to listen to cassettes and an FM station, so they go to a car accessory place and buy an AM/FM cassette player (the head unit). Their friend says, "Okay, I'll install it for you." The original speakers are 10 watt and the head unit has a 25 watt output, and the friend connects them to the radio, and the speakers go, "No way!" The woofer paper tears. So, they go back to the car accessory place and they tell the assistant and the assistant says, "Okay, you need more powerful speakers." So, they buy a pair of 25 watt speakers for the front doors, and, as it's a four channel output, they buy a pair of 60 watt speakers for the rear parcel shelf. Like how the original speakers were aligned to the original radio, the new head unit is mismatched to the original speakers, so, just like you align the speakers to the head unit, you align the person's genitalia to their brain.