If Parkrun wish to be inclusive of everybody without insulting and taking the piss out of women then they need to do away with keeping scores, having lists for male and female high scorers/record breakers etc.
It can be a non competitive, fun activity for all and everyone taking part just takes note of their own times/ personal bests and can compare against themselves or friends who take part if they want to.
However if Parkrun wish to have a competitive, public scoreboard then they need to stop condoning men who lie about their sex and compete as female and remove those records if they are reported to them.
Not a perfect solution but the fact they are currently condoning cheating says a lot about their attitude to women.
I suspect they don't want to get rid of the competitive element because for a number of regular park runners the competitive element will be what motivates them and keeps them interested in attending week on week.
So it appears that their solution is to continue discriminating against women and hope that most female park runners either don't notice or shut them up when they do.