There are people who register for parkruns under pseudonyms, often for safeguarding reasons if there is a danger from being linked to a location. For this reason, and the sheer scale of parkrun as a community based, volunteer led organisation with over 8m people registered globally, it does have to rely on people inputting their own personal details.
I would not oppose a trans category in the slightest, but suspect that it would go unused by this type of supremisist transwoman who thinks he is entitled to dominate women's spaces and he'd still select the female box.
On the day, it probably wouldn't be clear that there is going to be an issue with false course records being set, and it would emerge after the results were processed and published. It would therefore require HQ to have a reporting and investigation provision and amend statistically significant results.
At junior parkruns, the system will automatically pick up on inappropriate age categories and not publish the runner or include on their stats. At a 5k the results can be voided if runners break the u11 arm's length rule or dog policy if the RD is aware at the time.
I don't have an issue with transpeople participating in parkrun, but women shouldn't be excluded from attaining course bests and records by biological males, and those records should reflect the biological sex of those categories.
Unfortunately the politicisation of trans issues makes it very difficult for parkrun to say that we are for everyone which is a core value, but to also put in controls to alter records. Given the tendency that some trans-activists have towards literal violence (very much so in the case that the article is refering to), that also risks putting volunteers in a difficult and vulnerable position.
Ultimately parkrun is one of the most successful public health initiatives in decades. It's fair to address this issue and have concerns, but action like boycots have much wider detrimental consequences.
I'd love it if some elite women decided to go touristing and smash known false records though... alas I am very far from that league.