Immigrant non-citizens with residency are still obligated to register for the Selective Service even today.
Where it would get interesting is non-resident aliens, ala a Foreign Legion component.
Imagine being a Mexican national crossing over from Juarez in 1996 to sign up with the US army at Fort Blitz to get US citizenship, getting sent off to fight with the 3rd ACR in Europe (or the 5th ID), working your way back via Going Home to Red Star/Lone Star to find yourself in Mexico after the border moved north a few hundred miles.
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