@randygalbraith OK, so I don't want to have a go at you, but this bit...
Some diseases are sex related (breast vs prostate cancer). But in day to day life why in the world would I have concerns about the sex organs of another?...shows the underlying problem. We are still seen by well meaning, but largely wrong people as "male women" at best.
NO
Let's look at the two examples you mention: breast and prostate cancer. Medically transitioned trans women will have both breasts and a prostate. Both cancers tend to be strongly endocrine linked. Our endocrine systems run much, much, much closer to the "female" baseline than the "male" one.
In other words, we need breast cancer screening far more than prostate cancer screening. My chances of developing prostate cancer with zero detectable testosterone in my body are close to zero, but I have a family history of breast cancer and need mammograms regularly, just as cis women are.
And this is replicated in nearly any medical situation. If you took a blood sample from me and did analysis, pretty much all of my numbers (except testosterone, which would come back zero) would fall in the female range, not the male one.
We say "trans women are women" for a reason, and this kind of "yeah but..." is not only wrong, it's dangerous.
Now there are a few cis people in my life who get this, but in my experience most do not, and still do the "will pretend you're a woman but know you have the male essence" thing, and that's why I generally don't trust cis people. The support of the majority of them is conditional, fragile, and generally misdirected (e.g. "let's get trans women screened for prostate cancer! Yay!" - if you tried to find my prostate in the traditional manner, you'd discover that my vagina is in the way).