In short, they used to promote face-to-face interaction between infants and caregivers, saying it was crucial to the development of children. They didn't change their minds. They didn't come out with a study saying why they were previously wrong. They just removed the literature promoting it, because it contradicted their current mask push.
I also didn't understand the twitter conversation, but now that you explain it - You (and Allen) are drawing conclusions that go way beyond the facts.
The fact here is that Allen had once found a particular webpage, and was not able to find it with google. Websites are OFTEN reorganized, with stuff added, deleted, rearranged. There's no evidence given that the page was removed because of the need for masks today.
The page that was removed had been part of a project produced in 2012-2013. All parts of that project had been removed, maybe because it duplicates what AAP has elsewhere, or perhaps because it just seems outdated, or perhaps because it never belonged to AAP in the first place and shouldn't have been placed on their site. It was created by the Ohio branch of AAP, and is still available on their site:
http://ohioaap.org/projects/building-mental-wellness/Go down to Building Piece of Mind handouts, and it's the first in that list.
Before concluding that AAP removed this due to mask policies, you really need to examine the entire publication that was removed. One could as easily draw the conclusion that AAP no longer believes in the importance of mental wellness during the first 36 months of life.