President Trump doesn't seem to subscribe to that fallacy.
The Democrats' view seems to be that any woman will do (Hillary, for example, or Napolitano), while the Republicans' view, as with candidates for any position, is the right one for the job.
Really? What female has ever had a position of power over Trump, besides his Mother? Republicans apparently DON'T care about being right for the job, or have the appropriate experience and talent, because they put Trump in the WH, and approved whatever knot heads he picked to fill key positions.