To me it appears from the article that the trust wanted actual females if possible to apply (re-listed ad to widen the short-list in the job where women are underrepresented).
The complaints described in DM are by MRAs claiming it's discrimination. It is not a well worded ad, so they may have a point. If you 'particularly welcome' applications from certain groups you need to explain why, in the advert, clearly.
The trust, however, also seems to think that being female is an identity, which is worrying, but is not addressed in the article at all.
It seems that DM has mixed in rather different issues here, as half the article quotes men's rights groups complaining about the poor discriminated menz, and the other half talks about Stonewall-inspired de-sexing of women's NHS advice pages.