"current security context is not trusted" for job running as a SQL login accessing linked server
I fixed this by 1) removing the WITH EXECUTE AS 'user1' clause from the stored procedure and 2) removing user1 from the job -- it is no longer the owner or the "Run as user" of the job's step.

My final configuration is:


SQL Server Agent job owner is a sysadmin, not user1
The job's step "Run as user" is left blank
The step calls a stored procedure which user1 has rights to
execute
The linked server has a local/remote mapping for user1 with the
remote user and remote password entered. The username and password
are the same on both servers. The "For a login not defined in the
list above, connections will" option is set to "Be made using the
login's current security context".
user1 has the appropriate permissions to query on
the remote server. 
user1 does not need to have the sysadmin role or any such administrative role