What my ex did was effectively go through puberty for a second time. His voice broke, he grew hair in places previously unseen.
He didn't "get hold" of blockers, he was prescribed them. He then went through a series of horrendous surgeries, to realign his gender.
I don't "think" he passes well, I know he exists as a man. For the 820th time, he was on a mainstream dating show on tv. The person he was on a date with had no idea he had "previously been female". He has subsequently been in a same sex relationship with said person for 5 years, because (bizarrely and intrusively) all of the functions of his penis do the same thing a cis males does.
As to your point about changing rooms - if it were that simple, then why don't the majority of women have no problem with trans females changing in the ladies room? As you say, it's only an offence committed by "the pervier end of the population"
The whole trans thing on Mumsnet is hysteria whipped up by people with no lived experience, and I hope if your children ever go through this, you'll be far more accepting than you are online.