I moved my domain registrar from GoDaddy to Cloudflare and iCloud didn't like it. I could still send and receive but they kept spamming me messages saying something is wrong and I had to reverify. When I tried to reverify, Apple kept sending me to GoDaddy, rather than Cloudflare. Typically support were useless, trying to blame everyone but themselves. I fixed it in the end by removing the domain and re-adding it. It's a great idea but their 'admin' page is utterly useless for managing it properly.