I honestly can get behind the thought of going vegetarian (even though I would never do it), but this is something I can not get behind. And quite honestly I do not understand it.
In the end everything I am going to say about these things is that if you buy these things locally from a farmer or a friend or whatever it should be okay, shouldn't it be?
1. Chickens will lay eggs no matter what, it doesn`t hurt them and it is something they will have to do. Just be sure to buy those eggs locally from a farmer or a friend or get your own chickens, we have had chickens for decades. As long as the egg isn't "pregnant" (no clue how to call that sorry) it should be fair game to vegans shouldn't it be?
2. Same basically goes for milk.
3. We have many beekeepers here where I live, they protect the bees take care of them and to their best to keep them alive and well. We need bees to survive and I am pretty sure that we actually do not have natuaral beehives here anymore, they are all from the beekeepers and they support them selfes by seelling honey. Without the money from selling it they wouldn't be able to keep them alive. It doesn't hurt the to make honey and you will keep the alive if you buy the honey.
4. I honestly don't see a problem with wool, sheep need to be shorn.
5. Basically what @Bear-Man-Thing said about zoos.