I can't imagine any reasonable person wanting men in women's prisons or women's sports.
Agreed, although sadly there are some reasonable people who haven't necessarily thought it through. So the caveat would be "after really thinking about it", which many people actively avoid, because it can feel uncomfortable to do so. I personally found it an incredibly uncomfortable journey, because I wanted to support people who felt "trapped in the wrong body" but not at the expense of everyone else. I've now realised that I still can show this support, just in different ways e.g. supporting the implementation of the Cass Report and looking forward to the outcome of the adult care review. This means I'm not inadvertently including autogynophiles in my support.
I think the majority of the country do not want to see transgender ideology go any further and would actually like to see it reversed and definitely kept out of schools and away from children
The same caveat applies. Sport is probably the easiest one to think about, as it's obvious how unfair it is once you realise that the permanent effects and benefits (strength, speed etc) of male puberty can't be reversed, even with testosterone suppression. Thinking about the overreach in gender identity accepted as fact being reversed and/or it not being taught as fact in schools takes a lot more effort. The temptation to look away and think "it's such a small, marginalisd population, it's none of my business" is likely even greater. However, arguably it's everyone's business when there's a medical scandal on this scale. Hopefully enough people are waking up to this, so that what you describe above becomes reality. Unfortunately we're still seeing it being pushed heavily as fact in the media e.g. news reporting, TV shows like Hollyoaks, Heartstopper, Dr Who and Doctors. Until that stops, we'll still get lots of people believing that the kindest thing to do is to accept that it's important to validate someone's gender identity.