This is the crux of it really.
If you a member of this faith, then it is heresy to not be wholly and entirely biased and to reject everything but the followings of the teachings of the faith.
Which is fine, we're a multi faith society, we live in tolerance of each other.
But this is the only faith that requires such total partiality and rejection of all other views, and cannot permit open mindedness or following of other responsibilities or even the law or facts if they conflict with the beliefs.
And unfortunately this renders a believer in this faith unable to hold a post of responsibility that requires equality and impartiality. It's incompatible.
This is going to have to be faced by the government. You cannot ask a staunch Catholic to run an abortion service. You cannot ask a believer in gender ideology to provide an impartial health service that is open minded about the best interests of a child questioning their gender.
And the service is there for the best interests of the child. Not for the believers to enact their faith upon the child.