Do you have source for that claim? I tried to find that recommendation, but all I came up with, was this fact check [1]. According to the fact check the CDC did NOT change cycle threshold, and the thresholds used to decide if test result is positive, are not different for vaccinated and unvaccinated. The quoted 28 cycle threshold is apparently only used for deciding if a sample can be submitted for sequencing.

[1] https://www.politifact.com/factchecks/2021/jun/03/tweets/cdc...