The AAP and WHO both endorse this position, and I can't find a reputable leading health org that argues otherwise.
The more I read about the basis of the claim though the more confused I get.
Parenting advice sites all point out that it helps child immunity. But the underlying studies are based on the ingestion of immunoglobulin, which doesn't even survive digestion. So essentially it protects the esophagus against waterborne illnesses, ie, mainly those no longer common in the developed world. That definitely makes sense in terms of evolutionarily-relevant child mortality threats, but that context is always omitted.
Or you get claims of improved cognition, then find meta-analysis that can't reproduce any results after five years.
http://pediatrics.aappublications.org/content/early/2017/03/...
https://www.theatlantic.com/magazine/archive/2009/04/the-cas...
Parenting guidance seems full of replication crisis issues, even in the medical literature. That's been the most eye opening thing about becoming a parent... people's strong interest in parenting makes it hard to explain the poor state of the data on the topic.