@coureur ... I think Breeze is a great example to explore these questions.
There is provision within the UK Sports Council's Guidance for Transgender Inclusion in Domestic Sport to prioritise inclusion over fairness, where the objective of a sporting activity is inclusion.
Breeze was established to close the 'gender' gap in cycling between men and women and sought to overcome the barriers that prevented women from getting involved.
If the presence of male people is a barrier for a significant number of women, then Breeze may be failing in it's original objective.
What do 'people' want to happen - some people want female only spaces, some want spaces where female identifying males are welcome.
You also said: 'If an organisation, or an individual, wishes to organise an event of any kind and say that it is open to both women and transwomen, then that is their prerogative surely?'... lawful and unlawful discrimination is the subject of much discussion and we are seeing fewer efforts to create female only spaces in sport, despite the wealth of evidence that these female only spaces are crucial to increasing the participation of women and girls in sport, exercise and use of outdoor spaces.
Collectively, I believe that we have lost sight of the objective to encourage women and girls to take part in sport, for fear of engaging in the difficult discussions around inclusion.