Maybe think of it in terms of both sensitivity and specificity

Sensitivity: Proportion of all trans people who would say yes to this test, regardless of how many cis people also say yes

Specificity: Proportion of all cis people who would say no to the button test, regardless of how many trans people also say no

Imagine a sample of 100,000 people and let's say 1% are trans (99,000 cis and 1,000 trans). If sensitivity is 95% (i.e., 95% of trans people say yes), and specificity is also 95% (95% of all cis people say no), then that gives us 5,900 yeses and 94,100 no's

The yes breakdown: 4950 cis, 950 trans. 16% of the people who said yes are actually trans

The no breakdown: 94,050 cis, 50 trans. Only .05% are trans.

So, if you answer no, there's a pretty decent chance that you're not trans. Very rare for you to be wrong, it went from a 1% chance just on randomness to a .05% chance. If you answer yes, there's still a good chance you're not, but it's far higher than that initial 1% and so warrants further exploration.

Of course, the numbers were just made up. Change the 95% to 99% and you get 50% chance of being trans for yes and .01% chance for trans for no. I can't imagine many cis people answering yes, likely even 99% may be too low. There may be many non-binary, agender, etc.. people who would answer no, so the sensitivity would be lower for them

So, even if it's not a perfect test by any means, it still shifts the chances quite heavily, and can work well as a good initial indicator