You know, Stevie, I actually like your driving analogy.
Think about how we drive. Two cars approach each other on an ordinary road at sixty miles an hour, a combined hundred and twenty, with nothing between them but a painted line and a shared agreement not to cross it. Any driver could swerve across and kill everyone. We know this. We accept it. We don’t ban driving, because we weigh the real risk against the real cost and make our peace with the painted line. That’s what grown-up risk reasoning looks like. It’s never “could harm ever occur?” It’s always “how much, how likely, against what cost?”
Question: how do drivers know on which lane they are supposed to drive?
Answer: we've defined categories (you like that word, Stevie): on ordinary roads, you drive on the left. It doesn't matter who you are or where you go, just drive on the left.
Note: we don't let drivers identify into "having a right to drive on the right". Nobody can argue that because of where they are going, or what car they drive, or what speed they are going, or whatever, they can choose to randomly drive on the right.
Exceptions: exceptions are provided for specific cases when driving on the right is allowed: when passing a slower vehicle, in case of works on the road, things like that. Those are clearly defined in the law.
Danger: anyone who breaks the rules and randomly decides to drive on the right is rightfully recognised to be a danger to others. Note that this is the case even if there's nobody coming on the right. Just driving on the right is considered dangerous.
So now:
Question: how do people know which single-sex spaces they are supposed to use?
Answer: we've defined categories based on sex: male and female.
Note: people cannot identify into the other sex. Sex is biological and immutable.
Exceptions: exceptions are provided for specific cases, such as allowing little boys into female toilets.
Danger: anyone who breaks the rules and decides to randomly enter single-sex spaces of their opposite sex is rightfully recognised to be a danger to others. Note that this is the case even if there is nobody in that space at the moment. Just entering a single-sex space of your opposite sex is considered to be dangerous.
So, congratulations, Stevie, you've brillantly demonstrated why transwomen cannot go into fenale single-sex spaces.
You're a man. There's a white line on the road telling you to stay on your side. So stay there.