"Vaccine breakthrough cases are expected. COVID-19 vaccines are effective and are a critical tool to bring the pandemic under control. However, no vaccines are 100% effective at preventing illness in vaccinated people. There will be a small percentage of fully vaccinated people who still get sick, are hospitalized, or die from COVID-19."

Okay, they didn't say that's acceptable, specifically. But this lead paragraph on their website certainly gives that impression.

Further down in that article, we find:- "As of June 21, 2021, more than 150 million people in the United States had been fully vaccinated against COVID-19. During the same time, CDC received reports from 47 U.S. states and territories of 4,115 patients with COVID-19 vaccine breakthrough infection who were hospitalized or died." (emphasis added).

"Vaccine breakthrough cases occur in only a small percentage of vaccinated people. To date, no unexpected patterns have been identified in the case demographics or vaccine characteristics among people with reported vaccine breakthrough infections."

So they expect a certain percentage of people to be vaccinated, but then get ill and die.

At the same time, they say:- "COVID-19 vaccines are effective. CDC recommends that everyone 12 years of age and older get a COVID-19 vaccine as soon as they can.

• People who have been fully vaccinated can resume activities that they did prior to the pandemic."

Source:-

https://www.cdc.gov/vaccines/covid-19/health-departments/breakthrough-cases.html