There are a lot of really great people working for the CDC and they are doing some excellent work. They also made some bad decisions around respect to COVID-19 that absolutely does affect their trustworthiness.
However, if I add up the positives and negatives, they still are come out with a net positive rating for me. There's a lot more to the CDC than their COVID response.
This is one of my main qualms with how public health does their work. Lying is justified if you think it will convince more people to do something that will improve metrics at a population level. Maybe that works for a period of time, but once people find out, it destroys their credibility.
Break it up and scatter it to the four winds. Being heavily taxed for the "privilege" of being lied to is anathema to democracy, even if all the cool politicians, media, fossil fuel and arms companies are doing it.
The WHO and their fight against the idea that COVID is airborne is even more confusing to me. It felt like they didn't even want the idea discussed.