There are ways to become official citizens of a given country.Americans have their own country, culture, lifestyle, general behavior, that sort of thing. You can't just "become" American.
Brits have their own country, culture, lifestyle, general behavior, that sort of thing. You can't just "become" British.
Germans have their own country, culture, lifestyle, general behavior, that sort of thing. You can't just "become" German.
However, if you were to stick with the purely racial concept, then there really is no way for you to just “become” African-American, unless you actually have some of that racial heritage in your ancestry.
There really is no way for you to just “become” a member of the Cherokee tribe, unless you can prove that you have ancestors who were themselves recognized members of the Cherokee tribe.
So, in your game, is it a purely racial thing? Is it a cultural thing? Is it a political nation/state thing?
These would be important questions for you to answer.
Except being "Mandalorian" has nothing to do with species, so this is irrelevant.
Being a Mandalorian is about adopting a culture and a lifestyle; there's no logical reason that a Wookiee or a Barabel or a %&$#ing Gungan can't become one. The fact that the overwhelming majority of them are human has more to do with the fact that their culture is more or less limited to Mandalore, which itself is overwhelmingly human, rather than any sort of species bias.
Hell, if you really need some sort of mechanical acknowledgement of the Mandalorian lifestyle you're better off creating a custom specialization with its own career skills and talent tree.
Here's how I see it. You can be born Mandalorian, and that means that you come from the people who have lived on the planet Mandalore for generations, and have therefore a slightly different genetic makeup than your average correlian or coruscanti.
Or, you joined the Mandalorians or were adopted by one of them, and while you now have access to the same things a native-born Mandalorian would, your character's stats would not be the same.
Correlians are notoriously good pilots, that's the reason they get a bonus to piloting. Mandalorians are notoriously good fighters; I see absolutely no reason why a native Mandalorian would not have a bonus to melee or knowledge (warfare).
Mandalorians have been adopting people into their culture for a very long time; if you can fight, and they like you it really doesn't matter what race you are or what you used to do.
If it doesn't matter what species you are then why do you need a species stat block ? Especially one that uses humans as a base? It's completely counter-intuitive.