We have bought a domain name from a 3rd party and while they have change the nameservers without any issues, they can not change the tags. Every time they have tried it’s been rejected.
You need to add your domain to Cloudflare first. Then change the nameservers which aren’t set yet. (No Cloudflare nameservers are resolving for your domain, so if you have added the domain you need to set a plan or check you’ve correctly spelt the domain in Cloudflare)… https://cf.sjr.dev/tools/check?6186d47cb31b4bb5a7de81cbc3853393#dns
Once the domain is active on Cloudflare, only then can you change the IPS tag to transfer the domain registration to Cloudflare Registrar else, as you have found, the tag change will be rejected.
So it may be that the domain has been added to another account where it’s not active and (this is a guess and may not be the case!) that’s why Cloudflare is rejecting the tag change as it doesn’t know which account to tie the domain registration to.
If there is or you know that second account, you can log in and remove the domain from Cloudflare there, or wait for the domain to auto-delete from it, and return to just one nameserver set on Cloudflare to see if that helps.
Otherwise you can raise a Cloudflare Registrar support ticket and see if they can tell you why the tag is being rejected.