So nobody else is getting stutter in Battlefront 2 using AMD cards, I find that hard to believe.
There is currently an issue with AMD drivers which cause the GPU to run at 100% even when idle. This could be the cause for your stuttering.
The only fix I have found, is to run the drivers 17.11.4, which leads to the following issue...
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Since 17.12.1 there is an issue with a Shader Cache feature. File with cached shaders is not created for Battlefront 2. They are located under C:\Users\UserName\AppData\Local\AMD\DxCache\. It's causing the game to recompile shaders every time game is launched and every time match starts, it takes 100% CPU usage and the game stutters. I fixed it by simply reenabling Shader Cache in Global Radeon Settings (turn this setting Off and then set it to AMD Optimized). Now after running the game file is created in the folder listed above (for me on a driver version 18.3.4 it is called 9c6751e86c5a4c32dbf51da3d30919dc554615aba74be719.bin). Let the game run in main menu and on beginning of matches so the shaders get compiled and stored in this file (now it needs to be done only once).
RX5708GB, i7-7700K,16GB DDR4 2666,WIN10.