With new companion(s) also across a regeneration-boundary, they don't even know that this crazy person hasn't been a woman. Well, I think she mentions it in the train, IIRC, but there's weirder stuff going on that she lands in the middle of*, and at that point she's not even capable of giving her name. Later on she mentions she's not even human, and by that time nobody has any reason to object.
It might have been different in a different time and a different place (I'm wondering if the TARDIS field will hep, cover for that, as it does weird clothes, etc, except when the dressing-up box is arbitrarily raided** for… reasons) but this is contemporary urban Britain and she's dealing with two men who each know and love a strong, professional (medical!) woman who is also there, and leaps into the gathering storm of the adventure, plus the other strong professional woman who isn't going to question that aspect of this strange new person.
On past lives, canon (I think) has it that the First Doctor is the oldest age reached by the incarnation that is the boy seen in the flashback scene of (I think) young Doctor and Young Master traipsing off to stare into the naked Time Vortex in Sound Of Drums. (Or another time, but definitely referenced by Timothy Dalton arranging to contaminate the latter with the four-beat mindworm that contributes to him going mad like he always did... Timey Wimey!) And the count of Doctors (including the sometimes disavowed War Doctor and that bit where Ten regenerated into himself and dumped the metacrisis into the 'handy' recepticle) sort of matches the "twelve regenerations, thirteen incarnations including the original one" idea at the point when Eleven gets a much desired fresh set (another twelve?) from Time Lord HQ after that long stint on Trenzalore.
Though it's a dubious count, especially as during Eleven's time he gets a lives-saving dump of younger River's erstz regeneration-energy at one point and is "remembered anew back into the post-Pandorica universe" by Amy. Either of those things could mess up the tally as well. But Eleven is sure enough the limit was reached.. (Although Twelve's sort-of-7000 years of re-encountering The Veil in that castle in the sea must not have used anything up?)
I think any "buying women's clothing" might have been during Romana's companionship (as a courtesy for a fellow Time Noble?) or just for any of the earthgirls at some between-adventure lull. The several generations (of locals) of time in holding off the enemies on Trenzalore alone is long enough to have made that and Twelve's entire tenure the period the Doctor has not had a sniff of a ladies' clothing department. That also couldn't be accommodated by the TARDIS's cupboards.
Rose Tyler, at least, was initially directed to find the wardrobe "first left, second right, third on the left, go straight ahead, under the stairs, past the bins, fifth door on the left" or thereabouts, and has been actually seen in other forms before and after that point. Eleven initially reoutfitted himself 'in the wild', like Thirteen, but most of the others seemed to already have this wardrobe stocked sufficient for their tastes and also any passengers (many having been female).
But then we know The Doctor can be a bit of an unreliable narrator about his(/her) past, if we shift the blame entirely from merely the inconsistent/lore-ignoring scriptwriting, so who knows what the real truth is, and even if The Doctor is capable of keeping proper track of such stretched-truths!?!
* Coincidence? Or nascent story-arc, a la Bad Wolf meme or Missy appearing in the background to each tale?
** Often then to find they've actually landed in the wrong time/place/climate, And the companion still tends to get away with it, except where plot demands, while the Doctor tends to get a pass.