I got the geodir emails to be sent by removing the MIME-Version:1.0 from the header of the geodir email(s). (i.e. I modified the geodir email sending code).
According to the wp_mail reference: “…The [wp_mail] function will figure it out and will build the proper Mime header automagically.” So, the MIME doesn’t need to be specified. Other plugins do not set the Mime header. Other plugins are not setting the MIME in the header and they work fine with the wp smtp plugin. Could you check and update the geodir code to not set this MIME type?
ALSO, I found a geodir claim plugin bug: the claim listing email that is supposed to be sent to the administrator(s), is being sent to the ‘fromEmail’ as specified in geodir settings.
This is the incorrect line of code (in geodir_claim_functions.php):
$sent = wp_mail($fromEmail, $subject, $client_message, $headers); // To site admin email