is any of this comparable to banning any acknowledgement of the existence of trans and intersex people in anything connected to the federal government?
in fact refusing to define a term doesn't sound like banning at all. to ban is to forbid somebody else from doing something. to refuse to do something personally isn't banning.
Being unable to describe a woman would be pretty similar to banning trans acknowledgement. They're basically 2 sides of the same coin; the mismatch between reality and the categories we use. There are different opinions about which part of the mental model has to give. Ie, the concept of man/woman is too imprecise for political discourse - do politicians abandon the word woman or do they abandon the parts of reality that don't fit into a man/woman model?
The obvious solution is the third option of letting a few more genders in, but that would still require being able to articulate what a woman is.
The gender one is more consequential; if we accept that they exist there are a lot of women who get involved in the legal system because of their gender. Eg, say there is a case that involves gender discrimination - a judge that can't identify what a woman is will struggle to come up with reasonable rulings.
In fairness we don't have the words the judge used in front of us so maybe there was some hedging involved. But they do have to be able to come up with a working definition.
if the ruling is unsatisfactory, you can appeal. you can bring in expert witnesses. she's a professional, and she'll make her decisions based on the facts of the case, and hopefully not based on prejudice. if it's the supreme court, she won't be alone.
in fact refusing to define a term doesn't sound like banning at all. to ban is to forbid somebody else from doing something. to refuse to do something personally isn't banning.