Women are not 'fucking obsessed about trans people'. Women and girls are 'fucking obsessed' with campaigning to have their sex based needs prioritised over male people's demand that their gender is prioritised first.
And generally, yes, in real life interaction the majority of female people (children included) can correctly sex a male person.
Not because of what they wear or their foot size. Because of many other male body cues that do not change with 'transition. Just the face alone has many cues such as brow ridges, cheek bones, the proportion between the nose and top of the lips, the shape of the upper lip, the slant of a person's eyes, the hairline, the jaw line and so on. Hence it is rare even for those male people who have their entire face peeled off and sewn back on to 'pass' really. And as they get older, even with FFS the maleness comes back.
Then there is the skeletal proportions. The hips do not lie either. And therefore the q angles also impact the knees.
As a person with poor long vision, I can correctly sex people despite what they are wearing just by seeing them walk or run.
Male people seem like able to do this. And it is sometimes impossible with filters, photoshop and filters for images. Female people who change their bodies with testosterone are more difficult to sex in real life. But just because that is true, doesn't mean the male people are difficult to correctly sex at all.
So, if you like to believe in 'stupid conspiracy theories', great. I will trust the science.