It isn't always possible to pick and choose your clinician, patients have a right to express a preference and a right to decline care if their preference can't be met. It isn't possible for every healthcare setting to conjure up equal numbers of male and female clinicians to ensure everyone who has a preference gets what they want.
For example in labour we had a male midwife, he was fantastic and I had absolutely no preference either way, but if I'd have said no, I'm not having you, that doesn't mean a female midwife would have magically become available, and I'd have been shooting myself in the foot to decline medical care.
Interestingly patients tend to express preferences for things like GPs and nurses, but when it comes to intimate surgeries or examinations they are suddenly fine with a male consultant.
Lots of people misunderstand and believe patients have a right to their preference being accommodated. They don't as it's not possible for the NHS to promise they can fulfil that preference.
There are also plenty of people that really couldn't care less what's going on in the pants of the professional trying to help them, I'd say that's the norm.
In scenarios where we're considering trans clinicians then I think if someone asks for a woman clinician and the clinician available/assigned is a trans woman then that is something that should be explored with the patient. Is it important to you that they are a woman, or that their sex is female? If it's possible to fulfil their preference that they want a female/cis woman then great, if not, it's just the same as explaining there isn't one available so here are your choices: have the care delivered by a trans woman, or you will need to wait or find another place to carry out the procedure if there isn't anyone on staff that fits that person's preferences.
The NHS has plenty of trans clinicians that navigate this stuff day in day out.