I have had a go at unpicking some of the letter:
... transphobic hate groups and organisations such as Woman’s Place UK, Transgender Trend and the LGB Alliance.
Anyone claiming these groups are 'hate groups' are going to need receipts to prove it. What exactly have they said that is 'hate speech'? 'Transphobic hate group' sounds very emotive and dramatic, but where is the proof?
Transphobic groups have argued that to protect women’s single-sex spaces, trans women must be barred from entering them.
If transwomen use them then by definition they are not single sex spaces anymore are they, so it's not exactly a ridiculous argument? Also, a definition of 'transwomen' would be needed here? Are we talking about full on GRS and everything else that goes with that, or are we talking about 'any male who identifies as female'? It's a pretty important point.
They campaign against reforming the Gender Recognition Act, and claim that simplifying the process by which trans people update the gender marker on their birth certificate will result in a rise in sexual assaults against women. This is despite the fact that several countries have implemented similar reforms to their gender recognition laws without any negative impact to cis women whatsoever.
Well actually, Ireland (which is so often cited) does have exemptions for prisons as far as I understand, so even they know who is actually male and female.
These transphobic groups also argue against any gender-affirming healthcare for trans under-18’s and mislead the public into thinking that under 18’s are being given gender reassignment surgery on the NHS. They are not. A handful of trans teenagers each year are given puberty blockers, a safe treatment available to trans teens on the NHS since 1989. Multiple scientific studies show that puberty blockers are a life-saving treatment for trans teenagers who want them.
OK, this is the most worrying part. I can't find any information for when puberty blockers started being used on gender dysphoric kids, but I found that Lupron, which I believe is the hormone blocker used, was licenced for use in 1989, for prostate cancer. And then in 1993 for treating precocious puberty. It has never been licenced or tested for use to actually stop a normally developing puberty, its use for this is off label. Also, the NHS has recently reviewed its information about puberty blockers to say that their effects are not known and they are not necessarily reversible. Furthermore studies show that almost all children who start on puberty blockers later go on to cross sex hormones which are definitely more permanent. Also worth pointing out that Susie Green, who has signed this letter and therefore obviously thinks the idea of under 18s getting surgery is ludicrous, took her son to Thailand for surgery for his 16th birthday.
Trans men, women and non-binary people young and old have always lived among us. They have used the single-sex spaces that align with their gender identity this entire time.
It is important to say that if this has happened, this is because women have allowed this as a courtesy, not because of equality law. Under the current EA, women are entitled to single sex spaces. Sex is a protected characteristic in the EA. So is 'gender reassignment' but there is no definition of what this means and people seem to be applying it very loosely. Also there are single sex exemptions that exempt people even with a GRC. Stonewall is currently campaigning for these exemptions to be abolished. My knowledge on the legal stuff isn't as good as some on here, so someone else might be able to come along and further clarify?
The fact that you chose to make this a priority during the biggest crisis the world has faced in decades is even more disturbing. During lockdown, hundreds of women have been killed by abusive partners. Ethnic minorities are four times more likely to die from COVID-19. Surely these issues are more urgent?
Unnecessary deflection and manipulation. You could say this about any single issue.
I hope some of that is helpful?