Please explain in detail why you think that this paper shows that male people with transgender identities commit sex offences at the same rate in the UK as female people?
Because for safeguarding principles to be robust, female people should not have to accept a sub group of male people with a higher risk of committing harm to them than the general female population.
Also, why should female people accept inclusion of a sub-group of male people just because that group of male people might be a vulnerable group? There are many other groups of vulnerable male people and not one of those other groups get access to the female single sex spaces. So, this is a type of discrimination against those other groups of male people.
If a group of male people need special provisions for any reason, other than being children, the answer is not to include them in the female single sex provision. Because that provision is not a 'all vulnerable people' provision. It is sex segregated based on safeguarding principles which looks at risk of harm of that group's inclusion.
It is now well established that male people with transgender identities do not lose their male physical advantages. Therefore, even just the risk of physical harm to female people is higher in those provisions if they are included. It is considered reasonable acceptable risk for a female person to get away from another female person, this is not the case when the general male population (even after suppressing testosterone) has a recognised and proven physical advantage.
I look forward to your explanation as to what you think this paper says and why it is at all relevant for allowing a group of male people to access female single sex provisions.