I see your point but I don't see what strategy could have avoided the current press coverage. Feminists had to clarify the law to protect women in so-called critical spaces where they were being abjectly failed and discriminated against.
Since that clarification has been achieved, ultimately, the WI have to obey the law and evict their special male members. That is out of anybody's hands now. It was always going to reach the press and the trans brigade was always going to run the sob stories as far as they would go. This was unavoidable short of not meeting the fundamental objective of clarifying and protecting women's status in law.
Then - onto probably our major point of disagreement - the notion of non critical spaces. The problem is, so much of what isn't critical, can still add up incrementally to significantly harm women and girls' dignity, opportunities etc.
Sport is the easiest example. I do think for instance, never being able to win the park race, it simply not being possible to win biologically because you're competing against a man - harms amateur female runners. Harms women. And critically, only women. There is no impact on men. You have to understand that old men in their 60s literally beat women in their prime at this kind of level of competition and that virtually any man who has trained can beat the best woman there. It harms female participation. Women literally cannot compete.
And yes it's "just park run" but it still matters to (many of) the people who participate. If there are women who don't care about their performance competitively, and want to show solidarity with or have companionship with trans competitors, or any males - there is no barrier to them asking for and then competing within the same mixed race. But I personally think that if you run a racing event in which men and women participate, and which men have the option to win, then women need also to have the option to win. Not just to be accessories in a men's race. In principle it is wrong to invite women to participate in a women's race and then allow them to be beaten in that race by a man.
But outside of "just park run" / insert amateur activity - there is a knock on effect on competitive sport as well. Every competitive or professional sportsperson was once a child or an amateur, has filtered through a non/less competitive, less important grassroots level of sport. When women and girls are sidelined in the very limited single sex grassroots sporting clubs/events/activities that are actually available to girls/women - by boys/men who out compete them in a non protected "female" category or simply intimidate or injure them, that has an impact on their future prospects in competitive or professional sport too. It has an impact on every single women and girl watching and being inspired by female performance.
Just my 2pence