I had previously made this thread: http://www.gamesas.com/topic/1593838-crashing-when-it-rains/to document this problem.
I'm happy to report this problem is gone now with the Crimson 16.3.1 driver update. I have ran around for 30 minutes across multiple areas all when it starts raining without a single crash... usually I wouldn't last more than a couple of minutes, most of the time no more than 30 seconds.
Although the driver doesn't say anything about fixing this in the driver notes, someone from AMD on their support forums hinted that people having this similar problem in Far Cry Primal should try the driver and a lot of reports came back saying it had fixed the FC:Primal issue so I tested it in Fallout 4 and it seems to hold there as well.
So anyone who had this issue I fully recommend you go and update your drivers to the 16.3.1! remember to use Display Driver Uninstaller first just to be sure! Also remember to turn off the Power Efficiency setting in the drivers again when you're done.
Thanks.