When you send a boat into an end gateway, then place a boat quickly afterwards (during the gateway cooldown) and ride in it, it would send you to the other side but not the boat. The screen would rapidly shake and you are still in a seated position as if riding a boat. Shifting does not get you out of this. Changing gamemodes would, and would set you back at the previous gateway.

Steps to reproduce:

1. Put a boat inside an end gateway and wait for it to teleport
2. Put another boat into that same end gateway after the first boat teleports during the gateway's cooldown.
3. Mount the boat before it teleports.
4. You would get teleported to the other side while in a sitting animation as if you are still in the boat. The screen would also shake very rapidly. You cannot get out of this by sneaking.

Results are inconsistent, but this is the most reliable way to reproduce this in my experience.