Here is my config section that is working for me This will avoid running these two checks, I do not have anything here about authentication but your !authenticated = * should do the trick.
Code:
deny message = rejected because we do not want mail from $sender_host_address
sender_domains = !+local_domains
senders = @@lsearch;/etc/exim/reject-by-domain
deny message = rejected because $sender_host_address is in a black list at $dnslist_domain\n$dnslist_text
sender_domains = !+local_domains
dnslists = relays.ordb.org : \
relays.orirusoft.com : \
inputs.relays.orirusoft.com : \
sbl.spamhaus.org
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