No it is not illegal
Single-sex service providers can choose to exclude transgender people where there are ''proportionate means of achieving a legitimate aim''.
An example given by the Equality Act is that organisers of group counselling for female sexual assault victims could exclude a trans woman if they judged that clients would be unlikely to attend the session if she was there.
However, refusing a trans woman entry to the women's toilet in a pub is likely to be unlawful.
(
My Name was saying these words inside your head on, Sun 15 Aug 2021, 21:27,
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