Apple Private Relay impacts email deliverability through email address encoding and the necessity of domain whitelisting. Email addresses are encoded in the local part of the 'From:' or recipient address. Domain whitelisting is essential for deliverability; failure to comply results in bounces. Additionally, managing sender reputation, implementing email authentication (SPF, DKIM, DMARC), monitoring feedback loops, maintaining clean lists, and properly configuring the Private Email Relay service are crucial.