Identd has been not really been useful for a long time. Identd relies on the connecting host to confirm the identity (system UID) of the remote user who owns the process that is making the network connection. This may be of some use in the world of shell accounts and IRC users, but it really has no place on a high-volume SMTP server, where the UID is often simply “mail” or whatever the remote MTA runs as, which is useless to know. It's overhead, and results in nothing but delays while the identd query is refused or times out.

You can stop your Exim server from making these queries by setting the timeout to zero seconds in exim.conf:

rfc1413_query_timeout = 0s