Googling antinutrient with egg whites seems to bring up relatively few highly spurious 'paleo' type sites.
https://en.wikipedia.org/wiki/Avidin
Additionally, the protein in raw eggs is poorly absorbed, which could be because of other unidentified anti-nutrients. Again, cooking solves the problem:
There are people who eat raw or undercooked eggs. Not just some fad diet either, in some countries it's mainstream. In Japan it's common to mix a raw egg into rice or soup... very tasty and their eggs have a deep rich color in their yolk too.
I have a prairie oyster for breakfast sometimes: one unbeaten raw egg, a few dashes of worcestershire sauce, a little Tabasco, salt and pepper, and then you kindof eat it like it's a raw oyster. It's an acquired taste.
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But yes, the paleo theories mostly focus on it having some kind of effect on your stomach lining. It's a bit speculative. It seems they all point to this discussion as the original source: http://thepaleodiet.blogspot.com/2010/01/paleo-diet-q-29-jan...