add BLOCK_ICLOUD_PR=false to /etc/pihole/pihole-FTL.conf and restart pihole-FTL (sudo service pihole-FTL restart), ref the documentation.
Of course, Apple will advise you to use their DNS service, so they can get info about what it is you're doing with your devices, and build a profile (bye bye privacy). It's easy to claim things won't work if you don't, fear of that is almost always pretty convincing...
Read this topic, where things are explained, including the screenshots of the dialogs you'll be getting, if blocked, and the choices you need to make to avoid having problems.
iCloud Private Relay is basically Apple's implementation of oDoH (Oblivious DNS over HTTPS), the idea is you'll be using a proxy server (relay) to avoid the destination (DoH server) knowing who the request is coming from. Would be nice, if the relays would not be managed by Apple, thus not being able to collect the info anyway.
Be aware, by enabling iCloud Private Relay with the above setting, the devices will no longer be using pihole, thus everything will be allowed, regardless of the blocklists you have.
Also read this pihole documentation, here (unbound), where DL6ER explains why unbound is the best choice to get the most out of pihole, from a privacy point of view.