"...if there is guidance saying pander to men who say they are women to avoid violence"
Within the prison service (or at least for England and Wales) I don't believe there is any such guidance. This appears to be something just from this particular private company that was employed to do transfers.
Prison Rules are typically laid out in Prison Service Orders (PSOs) or Prison Service Instructions (PSIs). For example, there is PSO 4460 on how much prisoners must be paid when they are working.
If a prisoner is studying, working or training then they must receive at least £4 per week. In reality, prisoners can earn between £10 and £25 per week if they are working full time (the amount will depend on what they are doing).
If there are no jobs, education or training places available to a prisoner (or they refuse to engage) then there is a payment of £2.50 per week (50p per day).
Prisoners who have reached the state pension age and who do not work or take part in training receive £3.25 minimum per week (some prisons pay higher amounts to retired prisoners).
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But, to go back to your original point, there is HMPPS operational guidance on trans prisoners, but it does predate FWS.
Although the date given is 2024 it essentially dates back to 2019.
https://www.gov.uk/government/publications/the-care-and-management-of-individuals-who-are-transgender
The Care and Management of Individuals who are Transgender:
Operational Guidance
HMPPS Transgender Offender Team
Prison Operational Policy and Delivery Group
Version 3.0
November 2024
The guidance here goes into a lot of detail, covering both risks that the trans-identifying offender may be facing from others and also risks that this offender may pose to others. The guidance says:
"A proper assessment of risk is paramount for the management of all individuals subject to custodial and community sentences. The management of individuals who are transgender, particularly in custodial and AP settings, must seek to protect both the welfare and rights of the individual, and the welfare and rights of others in custody around them. These two considerations must be considered fully and balanced against each other."
[emphasis included in the original]
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However, going back to the Toshack v GEOAmery case, the guidance here clearly states that were the offender has a GRC then that must be used in place of sex:
"Where legal gender is determined, the legal gender must be recorded on all case administration system where ‘sex’ (male or female) is required."
But where there isn't a GRC, then sex is to be recorded accurately:
"Where legal gender cannot be determined, staff must record a transgender individual’s sex recorded at birth on all administration systems where ‘sex’ is required."