libpq is thread-safe as of PostgreSQL 7.0, so long as no two threads attempt to manipulate the same PGconn object at the same time. In particular, you cannot issue concurrent queries from different threads through the same connection object. (If you need to run concurrent queries, start up multiple connections.)
PGresult objects are read-only after creation, and so can be passed around freely between threads.
The deprecated functions PQoidStatus and fe_setauthsvc are not thread-safe and should
not be used in multithread programs. PQoidStatus can be replaced by PQoidValue. There is no good reason to call
fe_setauthsvc at all.
Libpq clients using the crypt encryption method rely on the crypt() operating system function, which is often not thread-safe. It is better to use MD5 encryption, which is thread-safe on all platforms.