Ugh, it's attitudes like that that would put me off parkrun, not running alongside people who are trans.
Setting aside the rest of your comment (I agree that pointing out mannish-looking women is unhelpful), I think you misunderstand the main objection if you think it's about women not wanting to run alongside trans people.
As a woman, I have zero issue running alongside trans people, men, children, buggies, etc.
My issue is that I can't compare my data to others of my sex and age range to see how I'm performing relative to key biological factors relevant to the activity. I don't care who else runs, but if Parkrun is going to collect and publish data based on various biological categories, it's only useful if it's accurate.
It's so disheartening for women who are trying really hard to see themselves slipping further and further below average as more biological males join their category and push the average out of their reach.