Not sure where you are from. But I guess there are plenty of users here that are banking in the US just on an ITIN without any issues (of course limted to the banks that accept ITIN for lending). I don't know any bank that would accept a US residency visa without a SSN as you are eligible for an SSN with such visa. And we all know that with a SSN you basically are open to anything in the US. There are very few credit unions that will still ask for more details︀ and want to see your visa. In most of the cases, a SSN opens you︁ all doors.
NFCU is for US military and their relatives only. Someone mentioned you may be able to get an account if you are referred by another customer, but I doubt this really works.