Well, yes, no metaphor is perfect, that's why they're metaphors. But no, somebody who lives in a country without being a citizen isn't necessarily living there illegally. You get a visa before becoming a full citizen, right? In the case of trans women, I guess that would be a diagnosis of gender dysphoria.
Yes, trans women are accused of reifying stereotypical femininity. I see how this is a catch 22. If trans women don't do everything they can to "look like women," they're perceived as men in dresses who aren't serious about femininity. The exaggeration, as much as anything, is cover. But yes, it's then perceived by some others as caricature.
What's changed recently, is that because the "trans umbrella" keeps growing to include transvestites and people who are simply gender non-conforming, we see some obvious fetishists also claimining womanhood. Kayla Limieux is an excellent recent example of this.
But characterising an attempt to differentiate between these people as "regressive gatekeeping" is exactly why more and more women are just taking hardline "no" attitudes to trans inclusion. If the trans community refuses to acknowledge that there is a difference between a transsexual woman and a man who happens to be operating in "girl mode" that day, or that somebody who looks like a man will make some women very uncomfortable in spaces that were built for women, don't you think that sends the message that the commmunity doesn't really care about women's boundaries or safety?
Yes, I think there should be "gatekeeping." Aka, I think a reasonable effort should be made to ensure that males who want to be legally recognised as females are serious and aren't going to be a danger in women's spaces. No such procedure is perfect. And yes, there will be some inconvenience for trans women in the interim. But "some inconvenience" is not hatred or bigotry or "conversion therapy." It's an example of the adult reality of life that you can't have everything you want, exactly as you want it, all the time.
Again, why is it that we recognise how unreasonable it would be for me to demand to identify as Japanese, but not that it's unreasonable for a man to be able to simply identify as a woman?
I honestly wish there was a simple answer to this. I sincerely want that "inconvenince to be as small as possible for trans women and for women. But it's the result of a society that differentiates between men and women. And the problem is, we differentiate between men and women for good reason. Mainly, the privacy and safety of women (who everybody seems to forget are also a marginalised group. Just a big one). Completely abandoning that differentiation, for the validation of less than 1% of the population is a tough sell. Especially when an extremely vocal minority of that less than 1% is busy abusing and threatening any woman who asks these questions.