The WDTV Live treaming and the XBOX One do not like each other.
If you try to connect the WDTV through the XBOX One you will just have a lot of problems. Green tints, hanging etc. Generally this manifests itself very badly when you try to use a servoce liek th BBC iPlayer or Netflix.
Msft XBPX one team say it is because the WDTV i snot properly handing the EDID information and sending YCC instead of RGB all the time.
Even if I set RGB low by hand it still causes problems.
As to issues with NetFlix, that content is secured with HDCP. Google “Xbox One HDCP issues” and you’ll see lots of reports with problems relating to the Xbox’s HDMI passthrough. I’m not sure if iPlayer is HDCP secured – maybe one of our UK folks will chime in on that.