I can’t talk specifics about CDC as I’m european but this way of acting was present in most of the countries around the world and I think it’s somewhat safe to think that it decreased masks demand to a certain point (1%? 20%? 30%?). Even in solid democracies with high trust like Finland they lied so that people wouldn’t hoard that much.

Also I IMHO doubt that Fauci didn’t know about mask effectiveness - sure, maybe he didn’t know the very specifics but it was kind of obvious back then it wasn’t going to harm and one could infer that it’d probably help somewhat (nowadays it’s clear). IMHO all authorities just agreed to transmit a similar message around the world so they could in the meantime arrange more mask orders and sort out the distribution as production speeded up while avoiding massive riots and/or poor masks made at home that could’ve been worse than nothing.