The problem with R9 390 series crashing in DX11 is not specific to just FFXIV. It is a driver problem that currently affects the 390 specifically DX11 games. I've already reported this issue to AMD back with the 390 series released in June. I even have a youtube video demonstrating the problem.

https://www.youtube.com/watch?v=JQN1tBxp_3A

The workaround is to disable hardware acceleration in applications that use it such as web browsers, VLC, outlook, media player, etc. Otherwise running the game in DX9 will result in no crash.