As far as the plans for all mixed sex toilets go, the H&S legislation is probably your best bet. It has far more teeth than the EA because it's criminal law and it's far more black and white. Either the toilets comply with regulations or they don't. If they don't, will they be fixed pronto or would your employers prefer to be prosecuted?
One thing I haven't seen used yet but I think might be useful in these sorts of cases is harassment under the EA:
Harassment
(1) A person (A) harasses another (B) if—
(a) A engages in unwanted conduct related to a relevant protected characteristic, and
(b) the conduct has the purpose or effect of—
(i) violating B's dignity, or
(ii) creating an intimidating, hostile, degrading, humiliating or offensive environment for B.
In this case, the unwanted conduct is making all the toilets mixed sex, plus embracing self ID on a whim and from the sounds of it, the training as a whole.
This conduct would certainly violate my dignity and create 'an intimidating, hostile, degrading, humiliating or offensive environment' for me.
Explanatory notes on harassment under the EA here:
www.legislation.gov.uk/ukpga/2010/15/notes/division/3/2/2/14
They also were proposing making everyone have their preferred pro nouns on their id badge but thankfully that got dropped.
This sounds hopeful, not everyone's swallowed their rohypnol. Also that your gay colleague was unimpressed with the training. He may have a stong harassment case as well, especially if they insisted on the word 'queer'. It's worth putting a few quiet feelers out among colleagues - can you raise the issues as a group?
If you work for a private company they are not bound by the public sector equality duty. Nevertheless, you could suggest a full equality impact assessment before any changes in policy as best practice. After all, if they're woke enough to fall for the transactivist agenda, why on earth would they not want to do what they can to promote equality across the board, throughout the organisation? 
P.S. I don't even pretend to be a lawyer. I believe there is a network of GC lawyers taking shape so if the SHTF, send out the bat signal.