Only 18% of the more than 1,300 adults polled said they have "a great deal" of trust in the CDC.
A call to develop separate measles, mumps, and rubella vaccines to replace the combined MMR shot is not backed by evidence.
Researchers say the investigational three-strain vaccine produced a strong immune response and was well-tolerated in its first human trial.
The group warns that under Kennedy more childhood vaccines will be in jeopardy.
For example, while overall coverage was 82% in Gaines County, the epicenter of the outbreak, school-based rates were as low as 46%.
The CDC recommends that toddlers receive the varicella (chickenpox) vaccine as a standalone immunization.
Supported vaccines saved a record 1.7 million lives, 400,000 more than in 2023, and made headway in conflict countries.
The Vaccine Integrity Project staff and advisors note the conspicuous and consequential absence of US health agency vaccine campaigns and annual vaccination reminders ahead of respiratory virus season.
Approval for the HHS secretary has dropped from a June 11 poll.
Timely receipt of MMR1 remained unchanged across the study period, at about 54%.