I couldn't figure out how to label this issue, so I've labeled it for a human to triage. Hang tight.

Hi, thanks for reporting!
The best practices in https://cloud.google.com/identity-platform/docs/web/redirect-best-practices need to be applied only for web applications that use the signInWithRedirect web SDK API. Hence, no action is needed for mobile apps.

If there are other reasons why you need this feature, could you please describe your use case and why you need this? Thanks!

@NhienLam Thanks, I could have been more clear perhaps. Reason is not that it doesn't work, but that it shows the default *.firebaseapp.com domain during the authentication flow. We would like this to show our own domain for branding/trust etc reasons.

Situation is therefore that a custom domain has been set up in Firebase, which indeed can be used for web apps, but mobile (OIDC) auth flows still visibly reveal the default Firebase domain to the end user, to my knowledge without any option to change this.

@skion Thanks for the update. We currently do not support custom domain on mobile. We have put this feature request on our radar, but we are unable to promise a timeline right now.

I have another good reason for using custom auth domains:
A customer had their firebaseapp.com and web.app hostnames incorrectly included in phishing blacklists (DNSBL), interfering with DNS resolution on "safe/protected" nameservers. The only immediate solution before removing those blacklist entries is to use a custom authentication domain.
Is it hard to implement this customization option? Are there other alternatives?

This is now available in the latest Auth version.