InputCommon: Make the "input gate" not racey.

Source/Core/Core/Core.cpp

@@ -72,6 +72,7 @@
 #include "Core/MemoryWatcher.h"
 #endif
 
+#include "InputCommon/ControlReference/ControlReference.h"
 #include "InputCommon/ControllerInterface/ControllerInterface.h"
 #include "InputCommon/GCAdapter.h"
 
@@ -1035,4 +1036,11 @@ void DoFrameStep()
   }
 }
 
+void UpdateInputGate()
+{
+  ControlReference::SetInputGate(
+      (SConfig::GetInstance().m_BackgroundInput || Host_RendererHasFocus()) &&
+      !Host_UIBlocksControllerState());
+}
+
 }  // namespace Core