I think we need to get away form this bizarre idea that it is all about who uses what toilet. It is a far bigger issue than that.
There are a lot of times and places where we are segregated by our sex Note - sex, not gender. Sex, in all its biological glory. Why is that? Because it was recognised that there are times and places where this would put women in serious peril or at a disadvantage or uncomfortable. Let's take the obvious ones:
Prisons are segregated by sex because women prisoners (who are largely imprisoned for non-violent crimes) would be at extreme risk from the male prison population (a great many of whom have been imprisoned for violent crimes).
Hospital wards are segregated because sick people deserve dignity and being in a near-constant state of undress does not make you feel comfortable around strangers. Being on an all-female ward can address some of that. Being on a mixed-ward can be stressful, and stress delays healing/recuperation. The NHS still has some mixed wards that it is trying to make single-sex because it recognises that that is how patients need it to be. Should they stop, and just mix us all in the same ward?
Sport is segregated by sex because your average man is bigger, stronger faster etc. than your average female. And the same comparison holds true for elite sportsmen/sportswomen. If sport was not segregated, no woman would ever win again. So what would be the point in taking up the sport at all?
There are times when women are extremely vulnerable, e.g. when fleeing domestic violence. These women need to be made to feel safe, and an all-female refuge goes a long way towards that.
Sex and gender are two different things. Sex is the biology that makes women smaller, weaker, menstruating, childbearing. Gender is the way you are viewed and treated by your society based on expectations of stereotypes you had no hand in shaping (and damned few conform to anyway) - so women are seen as frivolous, caring, bitchy and a whole load of other things which all add up to being less important than men. And being less important, all our hard-won rights are less important so we can just shut the fuck up about them. And unfortunately part of our gender is that we have been trained from birth to be nice to others, put their feelings before our own, share, be NICE. Which makes it quite difficult for a lot of women to say 'hold on a minute, something's not right here' - and so our gender conditioning is turned against us as a weapon.
The problem we are facing is that most people don't realise what a broad church claims the label of transgenderism. We should have guessed when the term 'transexual' disappeared and was replaced by 'transgender'. A transexual commits to being a woman - hormones, surgery, living as a woman. Transgender? Maybe - but maybe not. 80% of transwomen have a functioning penis. Some transactivists claim to be transwomen whilst presenting as men - I'm looking at you, Danielle Muscato. Yes, you read that right - beardy bloke in a suit and tie is a woman. Or there's Drummond who considers he's 'widening the bandwidth of how to be a woman'.
So, Maria Miller wants people to be legally women (on female wards, in women's prisons, competing in the Women's 100m race) based on their gender identity - 'feeling like a woman'. They will not be able to be excluded from female spaces, to do so would be illegal. So how many people are going to feel able to challenge an obvious male (e.g. Danielle and Alex) demanding access to a female-only space? And would that obvious male have to be transgender anyway? All they have to do is say they are - no proof is going to be required. Just their say-so. So we will be in the situation where any male, trans or no, can demand access to a female space - and he cannot be challenged.
Now I could be wrong (I'm not!) but this is just handing over female spaces, not just to transwomen, but also to predatory men. Or teenage boys who feel like havin' a laffff (we've only got to say we're trans bruv, they can't do a thing about it hahahahah). So effectively there will be no female spaces any more. Not one. And as for the transwomen - predators get off on the powerlessness of their prey. I could well imagine they'd get an extra frisson of power out of preying on a transwoman.
If this services.parliament.uk/bills/2016-17/genderidentityprotectedcharacteristic.html Bill ever becomes law we will feel the full force of unexpected consequences. Not men. Just women and transwomen.