I am unable to program Xilinx devices when a non-Xilinx device is in the JTAG chain in Vivado Design Suite 2013.4.
Set the following parameter in the Tcl console before launching the Hardware Manager:
set_param labtools.use_xicom_hw_server 0
Then, start the Hardware Manager, and confirm that you can program the device.
This issue is scheduled to be fixed in version 2014.1 of the design tools.