Of course it's possible to casually pass a trans person and not notice they are not their bilogical sex if they've done enough to conceal their naturally occurring physical sex identifiers. And yes, TM can often do this more successfully, as can young people.
I didn't say 'you can always tell'. You've changed my factual statement that it's almost impossible to hide all ones naturally occurring physical sex identifiers in a situation where sex is scrutinised; (a fact widely acknowledged by the trans community who often suffer much angst about this) to a statement you feel comfortable arguing with.
Changing my statement gives you an in to create a false equivalence with homophobia, on the very flimsy basis that some homophobes said 'we can always tell' about gay people.
When claiming that social behaviour and personality traits are reliable indicators of sexuality is entirely different from claiming to be able to look at a human being and identify their sex from their physical bodies. (Note, I'm not talking about being able to tell sex from assumed behaviour and appearance, like clothes and mannerisms. I'm GC and don't believe in stereotypes. I'm talking about physical features)
As for park run, while I agree with you it's a shame if something fun is overtaken by competition, this is something of a straw man given this isn't the point at issue. The point is whether TW should be treated as women in activities and spaces specifically designated for women. I believe not, as where an activity is designated for women, somewhere it has been decided that sex matters, and TW are not of the female sex. Argue by all means that there's no need for sex separation in PR or other activities where you claim males have no advantage, but that's an entirely difficult argument from one that advocates for some males to be exceptions.
Acknowledging the physical difference between men and women is not a gift to the far right or to violent men. In the case of the latter it is absolutely crucial to our protection from them. Failing to acknowledge it leads us into very dangerous MRA and VAWG apologist territory. Men denying their physical advantage and claiming reciprocal victim status is a popular defence already. Denying our greater risk of harm facilitates this.
As for the far right, pretending there are no physical differences between the sexes and that some men are women is what's been the gift to them. Because when left wing people say these things, the right use it as examples we are stupid, base our views on feelings not facts, are extremists and lunatics, and create an atmosphere of mistrust of the left in general.
I'm left wing, and my priorities are addressing class and wealth inequality, anti racism and the progression of womens rights. The fact that the people I'd expect to be prioritising those things alongside me have become diverted from the greater good to focus disproportionately on the rights of a subset of males is incredibly frustrating to me.