Although the Keepers of the Moon do have a connection to the Black Shroud, FFXIV is not like FFXI where each city was somewhat racially homogenous - Eorzea's citystates are very multicultural, in that even though a certain racial clan might have a strong connection to it's history, you'll find members of all races living there.

As for ACN, the class is stated as coming from the southern island continent of Mercaydia, which is apparently where the lalafell originated, but also there's a strong possibility (with little proof), that the miqo'te also originated there.

But really, the lore of the game in regards to the five races is very open - as I mentioned Eorzea is mulitracial and and a cultural melting pot, so feel free to create a Moonkitty ACN in Limsa. Worse case scenario you could state that he moved there to study Aracanima but was born elsewhere. (This is actually what I did with my own character's backstory - having her born in Ala Mhigo, yet growing up in Ul'dah where she learned swordplay as a GLA then moved to Gridania where she started her adventuring career at the start of 1.0).