Gosh, I had no idea quite how hung up (as it were) people are on the whole penis thing. It's all so muddled up, on so many levels.
I find it rather depressing that there is an assumption that those with penises somehow need to be kept away from those without penises in order to prevent the former attacking the latter. It is true, of course, that men are more likely to be sexual offenders than women, but the incidents of these offences happening in toilets, or changing rooms, or the like are very, very rare. Sexual assaults are far more likely to happen in the home, and to be committed by someone known to the victim (sadly, very often relatives.) It is possible that women fear violence in such places, but my fear of something doesn't give me an automatic pass to discriminate against those I fear, in circumstances where my fear is misplaced.
Race does actually work as an analogy. The best examples are the arguments used about black people in Jim Crow America. White people's of black people was used to keep them out of white waiting rooms, white toilets, white cafes, etc. And of course, occasionally crimes were committed by black people, and those crimes were used as an excuse to keep all black people away from all white people. But to do was statistically irrational and discriminatory... Something that thankfully civilised, right-thinking people now acknowledge. As I suspect, in due course, civilised, right-thinking people will acknowledge that the current hysteria over transwomen in women-only spaces is also misplaced, and a thin cover for simple discrimination and hatred of 'otherness.'
As a society, there is always a balance to be struck between many competing factors. We need to keep everyone in society as safe as we can, and we need to protect vulnerable groups, but at the same time we need to allow members of society to be as free as possible to do as they like. One person's freedom very often has an effect on another person's safety. If I am free to speak as I please, there is a chance I will offend someone. If I am free to drive my car, there is a chance I will hit someone. If I am free to walk the streets at night, there is a chance I will attack someone (clearly, there isn't. I won't. But no one else can know that with absolute, complete certainty.) If transwomen are allowed to use female spaces, there is a theoretical chance that this right may be abused by a predatory male pretending to be a transwoman. But there is a theoretical risk with every freedom. And how sad (and I would say, wrong) to allow that fear to stand in the way of the rights of the trans community to be protected and tolerated, by a welcoming, open and tolerant society.
A little more understanding and tolerance, and less hysteria regarding penises, would do us all some good, I think.