Have you been using insecure settings and just updated the MAC Mail to the recommended secure settings using TLS/SSL encryption?
The two email accounts that cannot send and that get the TT421 Authentication error - TalkTalk require email sending to use port 587 and TLS 1.2 encryption and outgoing mail authenticated by username (the full email address) and password of the sending TalkTalk email account.
Previously, you were using port 25 to send outgoing mail and no password authentication. If sending from a personal domain address you must use the outgoing SMTP servers of the personal domain hosting service not the TalkTalk servers.
If sending TalkTalk mail from a TalkTalk email account then the SMTP outgoing server must be linked to the TalkTalk email address you're sending from. The SMTP outgoing server settings obviously have a username and password for a different email account.
You probably need to save any wanted mail messages that are not in the online server mailbox, delete the 'non working' email accounts from the Mac and then set them up afresh so they each have their own dedicated outgoing SMTP servers using the TalkTalk recommended settings for TalkTalk Mail addresses.
The TalkTalk Mail Support Hub is your go to resource for information, guides and Community support for TalkTalk Consumer home broadband and MailPlus subscribers.
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Using TalkTalk Mail
Setting up TalkTalk email on a Mac PC using Mac Mail
