iCloud Private Relay can be turned off by your ISP (twitter.com)

iCloud Private Relay can also just randomly turn off because of connection issues, you can not configure it to fail in a safe manner.

Any network administrator can control the availability of Private Relay: https://developer.apple.com/support/prepare-your-network-for...

Since the blocking is done via returning NXDOMAIN it seems that an easy workaround for users is to use another DNS provider.