OP there's a lot to read around!
But the Cliff Notes version would be
Radical feminist have always been generally against the idea that men and women should have gendered lives with different roles because they are women or men. There is no obligation for a woman to like knitting, makeup, housework or child-rearing just because she is female. Or for a man to by hyper masculine, want to spend 60 hours a week at work and be naturally aggressive.
They see these things as imposed on us by the society we live. So what is masculine or feminine varies greatly around the world, culture by culture and by time.
So when a person who was born a boy grows up and says they "feel" like a woman, radfems get a bit het up because what does that actually mean?
Iy used to mean someone who had body dysphoria and felt they were in the wrong body.
Now it means someone who feels the gender side is wrong but they can feel totally OK in their own body.
So a man with a penis and a moustache like Alex Drummond can call himself a woman whilst wearing a skirt and rocking a rather significant beard. Alex can then say they are expanding the bandwidth of womanhood because they like to fix cars. And radfems find that a wee bit offensive.
The other recent change that has made this all such a big deal is that Stonewall is calling anyone who is gender variant or kinky part of the trans umbrella.
So while you used to have tiny minority of perfectly reasonable normal transexual women who got on with their day, had their penises cut off and made every effort to pass. You also used to have "perverts" who were not transexual and did not want to be seen as women but did want to wank in their wife's knickers or expose themselves in their panties to women on the side of parks.
These two very different groups have now been lumped under the same umbrella and understandably a lot of women aren't happy to think we should all accommodate all of them. Particularly when we had been accommodating the first group all along. This isn't new.