Why would anyone oppose this if getting people vaccinated is actually their goal.. There are many examples here to support the distrust, and all the opponents to the idea have is "they wouldn't change their minds anyways" which means that they aren't even trying.
Now if your first goal is to keep a malleable "yes man" in the CDC to create policies at the WH bidding, then I guess you would have reason to oppose removing Fauci.
Link: https://twitter.com/DrewHolden360/status/1420526431512244227?ref_src=twsrc%5Etfw%7Ctwcamp%5Etweetembed%7Ctwterm%5E1420526431512244227%7Ctwgr%5E%7Ctwcon%5Es1_&ref_url=https%3A%2F%2Fwww.foxnews.com%2Fmedia%2Ftwitter-thread-fauci-cdc-contradictions