His unkempt hair and scruffy beard, contrast with his clothes that look clean and well-cared for. Most Citizens just ignore him, preferring not to talk to someone obviously crazy in their eyes. Interestingly, Moore was not born a vault citizen but managed to gain citizenship presumably by passing the arduous citizenship test to gain access to Vault 8 and citizenship. He became a Vault City citizen in 2240.
In reality, Thomas Moore is an undercover NCR agent gathering intelligence on Vault City and smuggling its technology outside. His contact is John Bishop of New Reno, to whom the Chosen One can deliver a briefcase containing Moore's intel and a piece of VC tech.
Moore can be ratted out to Joanne Lynette, which ends up with him being permanently banished from the city and his citizenship getting revoked.
The Chosen One can mention that he is a threat to Vault City to Lynette and offer to kill him, however she will refuse. Pushing the issue will have him kicked out of Vault City and his citizenship revoked.