Oh cool, let's check out some TERF messaging:

Sport is inherently physical, so the different physiologies of the sexes matters. Whilst everyone should be able to participate in sport, the Sports Councils’ Equality Group’s International Research Literature Review states “There are significant differences between the sexes which render direct competition between males and females unfair in most ‘gender-affected sports’”. The peer-reviewed scientific literature found evidence that:

Alright, pretty reasonable start. We all want fairness.

On average, compared to age-matched females at any given body weight, adult males have:

• 40- 50% greater upper limb strength
• 20-40% greater lower limb strength
• 12kg more skeletal muscle mass [1]

Hold up, did we just use a study about (cis) adult males to argue that trans women shouldn't be allowed? Oh no, that doesn't seem very scientific... Well, I'm sure it's fine, let's check their references:

[1] Janssen et al 2000, Handelsman et al 2018

Okay, it's fine, I'll look them up myself:

Skeletal muscle mass and distribution in 468 men and women aged 18-88 yr

Okay well, that can't be right, their numbers are just coming from a comparison to men, they're just pushing the narrative that trans women and men are equal. Huh. Let's check their other reference:

Circulating Testosterone as the Hormonal Basis of Sex Differences in Athletic Performance

Wait, this study doesn't prove anything about trans women either. In fact, considering their comparisons of low and high-level testosterone in males, you could reasonably extrapolate that trans women on feminising HRT are comparable to their peers from this study. I wonder why the post didn't bring up that possibility? Ah well, let's move on, shall we?

Handgrip strength is often seen as a wider indicator human muscle strength[2] and mean maximal hand-grip strength over 2,000 European young adult males and females shows:

Oh, huh, still conflating cis men and trans women...

• Female handgrip at 329 Newtons
• Male handgrip at 541 Newtons
• Highly trained female athletes still have weaker hand grip than 75% of untrained male subjects [3]

Hmm, it doesn't seem very feminist to perpetuate the wildly inaccurate myth that the majority of males would outcompete elite female athletes...

Okay, so would you like me to keep picking this apart, or could we agree that it's scientifically unsound now? If any of these "facts" were relevant to the discussion of trans women in sports, I might (reluctantly) agree that there's a safety argument to be made. But I think what this conversation lacks most is empirical evidence. It seems that if an organisation like the one you linked above, who ostensibly want what's safest for all women, that they'd love to fund such a study that proves definitively what's safest. That they wouldn't care what the result was. So why have no studies into actual trans women been done?

I know this is quite anecdotal, but myself and most trans femmes I've talked too (who are on HRT) can describe the experience of losing that strength that comes alongside testosterone. If you want something more empirical, I have read countless instances of trans female athletes being unable to come close to matching their pre-transition Personal Best's. In fact, the gap between their pre and post-transition PBs is often on par with the gap between female and male results more generally. I can't recall a single instance where their PB went up after hormones. Whereas most athletes in their prime continue to push their PB higher.