When people try to upload logged in as anonymous, They get the message

553 Anonymous users may not overwrite existing files

In their cPanel, anonymous upload is enabled, and anonymous FTP is enabled in WHM too.

Any ideas?

m facing a similar problem

Maybe the Anonymous FTP account has only read access, rather than write. I would consult with your web host to see if this is the case.

If I am correct, anonymous FTP accounts only has read access and I think they can download files, too. They cannot upload anything. Correct me if I am wrong.

I think your right. I have seen it both ways, however.

in the client's cPanel,
under ftp manager > setup Anonymous FTP

Allow anonymous uploads to ftp://ftp.*.com/incoming and

Allow anonymous access to ftp://ftp.*.com

Are both checked.

BTW, I'm the webhost lol