Way before the TRA latched on to LGB they latched on to 'intersex' and the appropriation of 'assigned at birth' is just one recent example.
The earliest documented example I can find is Zoe Playdon's book, The Hidden Case of Ewan Forbes: The Transgender Trial that Threatened to Upend the British Establishment.
www.thetimes.co.uk/article/760484d8-5b8e-11ec-90d0-c463baf3512f?shareToken=bc415bffcc18345f3b68a0afa490a625
Forbes' family said he had a DSD and they were very upset by this book. What is clear is that people with a trans identity were abusing a law that was intended for people with DSD in order to change their legal sex.
Christine Burns helpfully explains how the trick worked (see images) and says it was going on 'at least since the early 40's' and how Corbett v Corbett closed the 'loophole' they were using. Also explains Christine and Zoe's work setting up the 'Parliamentary Forum' (precursor to an APPG?) which led to the GRA.
Then from the 1990's or earlier it was common for males who ID as trans to say they had 'intersex of the brain' or to confabulate 'intersex' histories. I believe there were one or two prominent sexologists (or allied trades) who spoke at the Gendy's conferences who encouraged this view. I'll see if I can find links tomorrow.
This 2005 essay by Kiira Triea, who had a DSD, eloquently describes the behaviour of these men:
'It was tiresome having to cope with sexual fetishists who were paraphilically attracted to "hermaphrodites" and transsexuals who imagined that they would be more socially legitimate as "intersexuals".'
www.transkids.us/learning.html
Press for Change and GIRES used to be part of the same organisation but in 2000, GIRES pissed off a load of intersex orgs through their attempts at forced teaming. Press for Change parted ways with them as a result.
I wrote about this in a few posts starting here:
www.mumsnet.com/talk/womens_rights/3463920-Lets-go-back-to-2007?page=5&reply=85165525
Most of the links in that thread don't work any more. You can get some of them to work by deleting the '"' off the end of the URL. Some others, it's worth searching for archived versions. But some have been memory-holed completely.
Everything's coming undone now and lots of people are keen to hide things they were very proud of only a few years ago, so screenshot and archive the fuck out of this stuff wherever you find it.
Glomming on to 'intersex' was important in the olden days to prove they were Not Gay. LGB was no use to them back then and they did what they could to distance themselves from gay men. See for example Beaumont Society's early ban on gay men joining:
www.beaumontsociety.org.uk/our-history.html
Fast forward to today, glomming onto LGB is far more useful for TRA (see the Denton's document) but 'intersex' is still useful when they want to pretend that 'sex is a spectrum' or that we are all 'assigned a sex / assigned a gender at birth'. They added an 'I' to the alphabet soup and a purple circle to their migraine-inducing flag and they divert funds from DSD orgs to LGBTQI+ etc. orgs because it's much easier for funders to tick all the boxes at once.