my dear friend, and i do count you among my one hundred million dearest friends, you simply must stop believing everything the Republicans tell you. that press release came from a Republican-majority House committee. it's in their interest to push a pro-Trump/anti-Dem/anti-CDC/anti-NIH narrative. why do you suggest the CDC to be untrustworthy for 'most likely' political motives when the Republicans certainly have them?
masks do help and precisely because Covid spreads by coughing, sneezing, and talking, in the same way that the flu does. they reduce the ability of unknowingly infected persons from spreading virus-bearing droplets efficiently. i don't find your 11 to 10% study, but i'll look at it if you have the reference. even if the effectiveness were only 10%, that would still mean saving many lives.
social distancing does work when infected people self-quarantine. however, if they go out in the world and stand just 6 feet away from others, well yes, that won't work very well.
immunizations were never billed as stopping the spread of Covid. the vaccines build immunity in individuals so that they stand a lower chance of becoming infected, have reduced symtoms if they do become infected, and experience more rapid recovery. for all of these reasons, transmission is also reduced. uninfected people can't transmit it and vaccinated infected people are less contagious than the unvaccinated.
this is mostly common sense, so the CDC is unlikely to change their guidance when NIH and their own data supports it. when there are disagreements between studies as to whether certain precautions should or should not be taken, i'll always err on the side of common sense.