Summary:
Ender dragon can fly into end (city) gateways and can cause unwanted behavior.

Description:
The ender dragon can enter end gateways, causing possibly unwanted behavior as the ender dragon teleport's to the end island gateway (the gateways away from the main island). Please keep in mind there is a currently a bug (MCPE-37590), that can cause the ender dragon to duplicate in some of these scenarios.

This can most easily be reproduced when the settings for render distance and simulation distance are set at there lowest values (RD=8 SD=4 in this test case). Both issues might be related for a appropriate fix.

When the dragon flies into the end gateway, the dragon gets stored to be loaded on the other side of the end gateway (near the end city islands).
This can lead to some problems:

1. The player has not seen the event of the dragon entering the end gateway (and has no clue where the dragon went) if MCPE-37590 is fixed. Only one short beacon like beam is shown to indicate the dragon has entered the end gateway.
   Currently this will cause the game to spawn a new ender dragon duplicating the previous (MCPE-37590). So the player can "finish" the fight (with a new dragon). However if the player is unaware this happened it can lead to the end (exit) portal not opening and the player not having a clue how to finish the fight if MCPE-37590 is "fixed".
2. Following the ender dragon through the same end gateway, can cause the game to both load the player and the dragon at the destination at the same time. As the ender dragon is stored to be loaded when the destination becomes active. Causing the player to be loaded near / inside the dragon and swung away by the dragon, most likely causing the player to die. For example dying in the void. Loosing all of the items the player is carrying.
3. The player managed to find the enderdragon in the destination portal (near the end city islands) by for example building to the end islands or previously mentioned (2). This can either cause:
   3a) The ender dragon flies back trough the same end gateway and reappears back on the main island (best case scenario). The target was the player, after being teleported to the end (city) islands the target is the main island 0,Y,0 causing this trajectory back to the main island inline with the end gateway.
   3b) More likely the ender dragon starts flying back to the main island (0,Y,0). With a low render distance and or simulation distance the dragon becomes "stuck" in unloaded chunks somewhere in the void between the main island and the end city island. It becomes extremely difficult to guide this dragon back to 0,Y,0. This can also possibly destroy player builds like enderman farms or whatever the player has build over the void outside the main island (as the ender dragon destroys most blocks it comes in contact with). It becomes extremely difficult to track the location of the dragon in survival (as every time it is loaded it tries to move closer to 0,Y,0)

Steps to reproduce:
Stand close or behind a end gateway in survival.
Have the ender dragon fly towards the player while standing close to an end gateway.
Make sure one dragon at least made it through the end gateway.

Observed behavior:
The ender dragon can enter end gateways

Expected behaviour:
1 The ender dragon can not enter the end gateway portals
2 The ender dragon can not get close enough to the end gateway portals causing her to teleport

Notes: It has been difficult to pinpoint accurate results with MCPE-37590 active as multiple dragons can appear.