The problem is with the software driver. The driver read/writes from the DPCD interface of the DisplayPort and the DDC registers of the HDMI using a port interface.
The port interface is common, but the functions for HDMI and DisplayPort are implemented separately. The port interface is mapped to these underlying functions.
If both the HDMI and DisplayPort are present in the design, then there is a conflict where the top level port interface functions are mapped to the functions of both HDMI and DisplayPort.
Users can work around this by running DisplayPort and HDMI on two separate platforms, such as two separate MicroBlaze instances.