This issue does not occur on my desktop with NVIDIA or on my notebook with Intel graphics.

I am using the latest Linux Mint. Steam will only work if I launch it as following from a terminal:

LD_PRELOAD='/usr/$LIB/libstdc++.so.6' steam

The default AMDGPU driver is being used (flgrx is deprecated and not available for recent hardware). The card in use is a Sapphire Radeon R9 FURY.

The output of trying to run Steam normally:

steam
Running Steam on linuxmint 18 64-bit
STEAM_RUNTIME is enabled automatically
[2016-11-26 20:31:41] Startup - updater built Oct 13 2016 00:47:16
SteamUpdateUI: An X Error occurred
X Error of failed request: BadValue (integer parameter out of range for operation)

Took a screenshot of my basic system information and included it as an attachment.