Ah, I think I see, gin.
I think the issue is, there are two kinds of prejudice people can have here.
One is bigotry - that covers, say, men who think a female doctor is an incompetent who'll kill them, or homophobic women who imagine a lesbian midwife is getting her jolliehs, or someone transphobic who just doesn't like trans people refusing a trans nurse.
It might be that the fear these people feel at the idea of being vulnerable to people they fear and distrust is perfectly real. But it's also reprehensible, and IMO there is an element of choice in it, even if it's conditioned. You can decide not to be a bigot.
The second kind of prejudice is, I guess, involuntary. A raped woman who's terrified of the idea someone with a penis is putting a speculum inside her did not choose to feel that fear, and if she's very traumatized, she probably can't control even physical reactions like shaking.
That's a much more appalling thing, which I guess is why we do end up focusing on the very unlikely cases, like a raped woman having to go for a smear to a trans nurse.
But I think that, when we discuss that situation, people confuse the second situation with the first - or even assume that the second situation is somehow not really serious (as I think that woman quoted in the article does TBH).