• Steam client version (build number or date): 02/10/2019
• Distribution (e.g. Ubuntu): Kubuntu 18.04
• Opted into Steam client beta?: No
• Have you checked for system updates?: Yes

I've got two separate Kubuntu machines (stock Kubuntu 18.04 with the latest updates), and this issue is present on both of them. Vagante won't read controller inputs unless "Steam Controller" is selected in the options menu, The Binding of Isaac: Rebirth will flip between keyboard inputs and controller inputs, and some Steam Play titles like Tomb Raider: Legacy and Tomb Raider: Underworld require me to force Steam Input off in order for the controller to work at all. Looking at the BPM controller settings, highlighting my Xbox One controller seems to indicate that it's being read as a Steam controller. Support led me here, perhaps because Kubuntu isn't officially supported even though Ubuntu is. More information can be found in the support thread here:

https://help.steampowered.com/en/wizard/HelpRequest/HT-4FNW-64VK-28PT

Steps for reproducing this issue:

1. Set up a fresh install of Kubuntu 18.04 and install Steam and the latest updates from the package manager.
2. Plug in an Xbox One controller and enable Xbox Controller Support in BPM.
3. Try navigating menus in Vagante, The Binding of Isaac: Rebirth, and Tomb Raider: Legacy and Underworld via Steam Play. Vagante won't work until the Steam Controller option is checked in the menus. The Binding of Isaac: Rebirth will flicker its button prompts on and off with Xbox Controller Support enabled, and it won't recognize the controller otherwise. Tomb Raider: Legacy and Underwold won't work until Xbox Controller Support is disabled or until you force Steam Input off for those individual titles.