Haven't read the article, but I welcome the commitment to keep the schools single sex. I went to a girls' school from the age of 11 and so did my daughter. I feel it was beneficial in both cases. There are pros and cons, but on balance the absence of boys and having a mainly female staff was a good thing.
I thought Eton came out a couple of years ago and stated firmly and clearly that they would remain single sex, so no transboys to be admitted. Oddly enough, they haven't been relentlessly attacked over this. 
It's my impression that a significant number of parents who choose single-sex day schools do so for religious reasons, especially girls' schools. I assume they would think again if it turned out that the school had started admitting male pupils who would be in class and changing rooms with their daughters.