People seeing something as transphobic and it actually being transphobic are two different things though.
She's not "outing" anyone as biologically male because by definition, a trans woman can only be biologically male - otherwise it would simply be a woman.
She acknowledged that the person identifies as a woman. But your personal identification preferences do not erode biological fact. So rather refreshingly for a politician, she's answered clearly with actual, proven, scientific facts.
If people want to take offence, that's their choice but you can't deny the existence of biology, and it's ridiculous that biological fact can't be mentioned because "transphobia".
I don't see any correlation with the example you gave about a British-Asian only wanting to identify as British - that's nothing like the same thing at all. The "Asian" suffix is unnecessary because the person is still British regardless of their skin colour. A better example would be say, a French person, born in France and whose home is in France, saying they identify as British. Well, fine, no issue with that if that's where they feel ideologically at home - but they're still actually French.