Summary: My organisation moved from Exchange to Office 365 For years the SQL Database Mail has used Local SMTP (with a spf record to stop mail being flagged as junk) The instant that Office 365 was enabled on the email address that SQL had being using (and obviously the DNS records updated), mail been to queue on the local SMTP Relay; only for some destinations but let us assume the emails that passed had limited reverse lookup. I have configured Database Mail to use [mydomain].mail.protection.outlook.com with port 25 and 587. I have created a Mail Connector using the Exchange Admin Centre. I have set local SMTP (through IIS6) to send directly (no smart host), and to use [mydomain].mail.protection.outlook.com (which should relay through the connector). Whatever I do mail does not leave my server. Support requests (both free and paid for) to Microsoft reach the "I'll get back to you" point and then go quiet.
I have struggled with Database Mail before and found a way past all the inherent protections against spam. This seems to be a problem around what Office 365 expects and I am unable to "tick the correct boxes".
Office 365 doesn't allow anonymous SMTP relay. You must authenticate to send mail. Obviously the issue here is that would require using up a license. The preferred way is to pay for a third-party SMTP relay service. We use SendGrid to accommodate Database Mail because we also use it for email marketing campaigns. If your mail volume is small, like 100 or less emails per day, SendGrid is free.