Healthcare accessibility is an important issue. We know from trans org stats that there are high levels of mental health problems amongst trans people as a group, and there is a higher likelihood of living on the fringes of society due to discrimination around jobs / housing / etc.
It is also well known that in the UK we have high numbers of people who have issues engaging with assistance whether due to low reading age, language issues, learning disabilities, mental health issues, substance abuse issues, the list goes on, and there is no reason to believe that the trans population differs from the general population in these regards. Apart from maybe being more likely to have some issues according to my reading.
The glib "oh they're not stupid it's all fine" when the issue is people not receiving calls to attend screening for diseases / conditions that they might be susceptible to is very callous and dare I say it not very inclusive, which is odd as I assume you are trying to be "pro trans" with this point.
There is also the issue that sex specific things can be triggering for trans people and obviously very much so, this is the reason they are lobbying hard to have words like pregnant woman replaced with pregnant person etc. Your idea that all trans people will be AOK with firstly knowing they need these tests even when they are never called, be proactive and willing to put themselves forward to make the appt, possibly have to explain to receptionists in crowded waiting rooms why someone who looks like a bloke is here for a smear etc etc
OBVIOUSLY this is not good enough and will lead to people not accessing healthcare they should be.
The answer is as mentioned upthread to have a sex at birth marker and something to over-ride the calls if a person has had surgery that makes it no longer an issue.
Bizarrely though I think more extreme TRAs would be against that as they say they have always been the sex they identify with and so any records otherwise need to be expunged even from healthcare but that's a different issue really.
I find your comment very unconcerned about a group containing some very vulnerable people.