Short answer
Set up a custom SMTP provider in the Auth settings, with the host, port, user, password and a From address from your email service. After that, confirmation, magic link and reset emails go to any address. For a quick test before then, add the tester to the organization’s team.
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Why the email is refused, and the fix
01
The project uses the default SMTP service
“Email sending is not allowed for this address as your project is using the default SMTP service. Emails can only be sent to members in your Supabase organization.” Supabase docs, Auth error codes (email_address_not_authorized)
Supabase gives every project a starter email server for testing templates. It refuses any address outside the organization’s team, which is why your own sign-up works and a customer’s doesn’t.
02
Custom SMTP was never set up for launch
“This server imposes a few important restrictions and is not meant for production use.” Supabase docs, Send emails with custom SMTP
Pick an email service that supports SMTP, verify your sending domain there, and enter its SMTP settings in the project’s Auth settings. Supabase names services such as Resend and AWS SES as working options.
03
A tester is not on the team
“Unless you configure a custom SMTP server for your project, Supabase Auth will refuse to deliver messages to addresses that are not part of the project's team.” Supabase docs, Send emails with custom SMTP
Before custom SMTP is live, only team members get email. Invite the tester in the Team tab of the organization settings, or wait until SMTP is set up.
04
The rate limit hits next
Also check: the default service also limits sending, currently 2 messages per hour. Once custom SMTP is saved, Supabase starts the project at 30 messages per hour, which you can raise on the Rate Limits page.
Checked against the vendor’s docs on : Supabase docs: Auth error codes; Supabase docs: Send emails with custom SMTP.
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Related: Supabase Email address invalid · Supabase email rate limit exceeded · Supabase auth emails going to spam · Supabase Email not confirmed