I feel as though the discussion keeps shifting now and thats not a coincidence.
It started with claims about male gynaecologists themselves, then moved on to patient preferences, then workforce ratios, then sexism in medicine, then trauma, and now mammographers.
Those are all separate issues.
I completely accept that some women strongly prefer female gynaecologists, particularly if they have experienced trauma, and I agree that sexism in medicine should be tackled wherever it exists.
However, neither of those points demonstrates that male gynaecologists are unsuitable, nor do they support the original implication that men enter the specialty for inappropriate reasons or that they should be in "the minority".
The reason I keep returning to the study you posted is that it simply doesn't support the conclusions being drawn from it. It tells us about patient preferences. It doesn't tell us what the "ideal" workforce ratio is, and it certainly doesn't tell us anything about the motives or character of male gynaecologists.
It feels as though we've moved a long way from your original claims, which suggests those claims were harder to defend than the later points about patient choice and trauma and so its not surprising you keep bringing up new issues.