I'm sorry you're having this experience with your DH talkingdeadscot.
I don't know your DH, so I don't know what he's generally like, but I had similar conversations with my DH a couple of years ago and he did not understand the issue either. Same with my adult sons.
There's a lack of understanding that comes from a lack of experience and that was certainly happening in my family. I did eventually get through to my DH and I know he really gets it now after listening to him explain the issue to fellow business men at a big birthday bash last year.
What I would recommend, beyond the many good tips you already received, is to make it easier to focus on what matters by being careful with the terms you use.
I do not ever use the words transwoman or transman. The way our brain works, we focus on the root word, which in this case fudges the issue.
I speak of males and females (female people or male individuals or female person or male doctor etc) and males/females who identify as trans.
So I start with the basic premise:
Female people in the UK have the right - in language and in law - to define themselves in a category of their own, separately from males. All males.
From this right derive female-only spaces, services and provisions. Sports, scholarships and awards, educational programs, prisons, rape crisis centres and refuges. Political positions and women's rights groups.
If he rejects that premise, don't waste your time arguing about what makes males who identify as trans female. I would first focus on why we have CEDAW, an international human rights treaty to eliminate discrimination against women and girls, and why Article One of this treaty roots this discrimination in our sex.
If he understands why female people need separate and specific protections, then you can move onto arguing why we must be able to exclude all males from accessing these protections, regardless of their identity.
So I would ask my DH to explain why one subgroup of male HCPs is exempt from the restriction female patients are allowed to place on all other males when no other subgroups of males are (same-sex attracted males for instance)?
I also don't use the word gender in debate. I use sex stereotypes and sex role stereotypes. I don't talk about gender identity but about personal preferences for the sex stereotypes and sex role stereotypes associated with a particular sex.
And if necessary I explain why these stereotypes are harmful to all female people and what it means to enshrine them in law or policy.
I explain that policies that allow the inclusion of one subgroup of male people in female-only provisions of necessity lead to the exclusion of several subgroups of female people from those provisions. And I ask where they will be supported. And how that same subgroup of males will then be excluded from any new female-only provisions specifically created for the subgroups of female people excluded from mixed-sex provisions.
I hardly ever discuss how males who identify as trans could possibly be women or what makes a woman or anything like that. I state my definition (adult human females), but since I only ever talk of female and male people, I don't see a need to spend any more time on that argument.