This kind of thing is increasingly a problem, especially in universities, and it points to some real issues with the whole project of treating identities differently. There are real advantages in terms of gaining positions if you can claim to be a member of a minority, at least in North America. Want to get on a great research team doing some important scientific work with a prestigious professor? Their grants now require them to hire based on diversity quotas.
You also get people who do have the relevant DNA, but no connection to the culture - I know a fellow at my university hired what must be two years ago now, who has indigenous ancestry - he told me he's never considered himself indigenous but when competing for a position, he couldn't afford to not mark it down. Great for him, I guess, but shitty for the poor bugger who just has to compete on his merits.
I keep coming back to this on the issue of gender ideology - it's not going to be defeated until this id politics approach is defeated, and that includes where its found within feminism.