I agree that there is room for expanding male spaces to those who are feminine and many people would benefit from unisex accessible single-space facilities. People have fought for them for years because there are issues with sexed facilities. Turning our current sexed toilets and changing rooms into unisex spaces without even paying for proper attendants is laziness, cheapness, and fake progressivism. Same with the issues of the prisons, just putting trans people into a different space with things as they currently are rather than having separate units. It's people wanting to appear progressive while doing as little as humanly possible. People love to throw 'what about trans men' when it comes to toilets and other facilities - but I doubt they really think trans men would be better off in men's prisons.
We can sometimes choose to ignore leering and push past our feelings, that doesn't mean we entirely choose to be sexual entities. My then-7 year old didn't choose to sexually harassed and threatened. 1-in-3 school girls don't choose to have to deal with sexual harassment while in uniform. Feelings are an extension of our senses, they react, we don't get to choose what we do and do not feel anymore than we decide what our other senses pick up. We can typically decide what we do with those feelings, but we shouldn't act like women's feelings aren't already routinely dismissed and ignored when it comes to public spaces and more needs to be done to prevent women being further shut out of public spaces.
And, I know it's moved on from this and this has turned into a babble but as an intersex person - yes, intersex people have a wide range of beliefs and attitudes; however, almost every intersex activist and education organization has made a point of discussing that while there is overlap with LGBT+ and intersex people, there are major differences that are erased when intersex people are brought into discussions on trans issues and it is quite harmful to intersex people to use us as debate pawns to shore up a side on trans issues so most of us prefer not to be involved in them. From the world's largest, the ISNA, which treats intersex and dysphoria as medical conditions and are aligned more with disability rights to it's practically political opposite Oiii, it's UK branch is UK's largest intersex group which treats intersex and being trans more as natural variants, align more with LGBT+ rights though makes clear that they don't see us directly in that, they have all made the point that trans issues and intersex issues are different because we're all quite tired of them being mixed up and being brought into trans issues discussions never helps intersex people - in fact, we're regularly told we're "taking shots" at the trans community when we fight for our own rights like being against cosmetic surgeries in minors when really we just want to be viewed as we are and not seen or treated as an extenstion of trans communities to be brought out as they see fit. Even those of us who are also dysphoric don't want our situation to be used as evidence in trans issues. I'll take someone who respects my sex and actually uses intersex people as a source on intersex issues over someone who calls my body a grey area or that my DSD is relevant in any way to trans issues any day of the week. I'm sure anyone can find an intersex person who likes being brought into trans stuff but ignoring our communities to cherry-pick those is prioritizing those that make life easier for non-intersex people to use us over the majority of those who have worked their lives to make things better for us.
Sports segregated by sex makes space for intersex people because we have a sex. We are either female or male. Really, in all the intersex groups I've been in, the thing that seemed to piss people off most is those who were disrespectful enough to try to erase our sex. We're not a grey area, the knowledge of our sex is vital to our well-being and medical treatments. Some intersex conditions are lethal without treatment and many are life-limiting with treatment - cardiovascular and skeletal issues are very common alongside the obvious endocrine ones - so this is very important.
Our issues in sports has more to do with a lack of access to medical access and knowledge as our conditions are often hidden from us which puts people into a shock finding out when older after years of training (both ISNA and Oiii support children knowing their sex and condition and treatments from an early age, far too many are told they're undergoing treatment or taking medication for other things) and a lack of consistency and a segmented rather than holistic approach with the rules - so sex hormone levels being the be all and end all measurement rather than having multiple measures is an issue. Also, the media's lack of knowledge is a big issue. This applies to many other athletes as well and many are trying to make better systems.
There is room for mixed-sex competitions - I did so quite a lot when I was younger, I competed in wrestling in high school on an otherwise all male team - but there is no need to ignore the differences between the sexes on behalf of intersex people and single-sex competitions and records will continue to be vital. We have additional medical needs but we're not that different even genetically - a CAH woman with the highest amount of virilization is less than a billionth of a percent different than a non-intersex woman and the push by too many to act like we're entirely different is harmful.
We're not a gotcha, we do not disprove sexual dimorphism in humans, we're not really a complication (there is no intersex gamete and lack of gametes has never precluded someone from their sex), and when it comes to trans issues, the intersex communities are often at odds with many loud/more visible parts of trans communities than we are on the same page even when we disagree with each other as intersex people.