Can pg_hba.conf trust processes? Is it possible to configure PostgreSQL such that it can trust a single process, instead of a specific user?
That is not possible I am afraid of.  The selection is based on the following criteria:


Type of connection (local or network)
Username requested
Database requested


Nowhere in there is a process given.  If you want to trust a given process the way to do that is to have a service account, a specific database user, and map these in, using peer authentication on *nix (peer on local connections used to be called ident but this was changed since ident is very different on network connections and has far more issues).