Another update.
Something changed. Now I can join any world that my friend is in, but he can't join a world that I'm in. This includes realms.
Examples (over LAN):
I am in my world, friend tries to join, he cannot.
Friend is in his world, I try to join, success.
I am in a shared realm, friend tries to join, he cannot.
He is in the same shared realm as above, I try to join, success.
Also, we just tried again today.
Attempted to join through XBOX, we got this error message: "Unable to authenticate XBOX Live account"
Attempted to join through LAN, we got this error message: "Unable to authenticate XBOX Live account"
Attempted again to join through LAN, we got this error message: "Unable to connect to world"
Yes, my friend and I have been attempting this over Wi-Fi. We don't have ethernet cords.
Another update:
Tried again with a different friend who has a different laptop and xbox account, but on the same wifi. I can join their world via LAN or XBL, but they cannot join mine over either.