A resposta está no artigo que você vinculou: use um agente de envio de mensagens autenticado e criptografado.
No entanto, isso limitará sua capacidade de se conectar a MTAs na porta 25. Presumivelmente, isso ocorre por padrão, pois há clientes menos atentos do Azure contribuindo para o problema do lixo eletrônico.
Recommended Method of Sending E-mail
Microsoft recommends that Azure customers employ authenticated SMTP relay services (typically connected via TCP port 587 or 443, but often support other ports too) to send e-mail from Azure VMs or from Azure App Services. These services specialize in sender reputation to minimize the possibility 3rd party e-mail providers will reject the message. Such SMTP relay services include but are not limited to Exchange Online Protection and SendGrid.
Use of these e-mail delivery services is in no way restricted in Azure regardless of subscription type.