Don't use the cloud if you care about privacy, or encrypt the data yourself before uploading. Has always been the case.
In fact, given that Apple do not E2E encrypt backups and already implement CSAM functionality by scanning data in iCloud [1] it's not clear what the purpose of the new PSI/CSAM system is. Which leads many to speculate that it's only purpose is as a prelude to scanning all offline content.
[1] https://nakedsecurity.sophos.com/2020/01/09/apples-scanning-...
It was never going to stop at iCloud uploads.