What country can they change their sex on a birth certificate?

It's not going to be soon. The transgender movement is part of a larger woke movement that is extremely tyrannical. You aren't allowed to talk about reality if it deviates from the narrative (feminists can certainly be guilty of this too). It's tangled up with post-modernist thinking where they believe language helps construct reality. So saying transwomen are women makes it so. And it's tangled up with identity politics/political correctness, where the most victimized, most marginalized just by these huge group labels like trans gives them power. Identity politics might have done some good at some point, now it's over stepped itself and instead of treating people like people, you are forced to see them as their race, gender, sexuality, etc. Right now these groups have a lot of power over the culture in western societies.

I don't think it will be soon. The grip that identity politics has on society right now is so strong. You can't talk about the actual reality of biology because trans people are marginalized. Their inner "truth" is sacred and respected by woke people. It doesn't matter if it's not real. Some of them even think logic, science, the whole enlightenment is White man's invention and that other culture/races have their own sort of truth that should be respected. (yes, that is stupid and pretty fucking racist, sexist)

It's deeply ingrained. The turnaround isn't going to be soon. But biology is real and sex is immutable. It doesn't matter how much they change their bodies or bully others into saying transwomen are women, they won't be real women. When their bones are dug up their dna will say male.