The CDC's report is a fantastic example as to why the CDC don't deserve our trust. They are dishonest. They cherry pick data to fit their narrative. They are unburdened by the constraints of peer review. They admit in their own study that it can't apply causation and yet they remain silent as the media run wild and report the study as causative fact.
This analysis has, to my knowledge, not been debunked at all: https://arieh.substack.com/p/inside-israels-delta-outbreak-p....
It shows natural immunity far outclassing vaccine immunity in Israel.
In terms of peer reviewed studies, they all show that natural immunity is fantastic:
https://jamanetwork.com/journals/jama/fullarticle/2781112
https://www.thelancet.com/action/showPdf?pii=S2589-5370(21)0...
https://www.cell.com/cell-reports-medicine/fulltext/S2666-37...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8209951/pdf/RMV...