Yes, and for some odd reason a lot of folks I know who are lactose intolerant are also slightly allergic to eggs..

Yes! Never really thought to question it though... now I'm re-thinking everything I thought I knew about food clarification!

I had attributed that to our fuzzy food categories. Some of which are due to how ingredient usage doesn't map well to botany, some is just marketing.

I suspect the perception of eggs as dairy could have shifted for practical reasons: lactose intolerance became more visible, and we needed a short way to say milk and milk products, without using the word milk.