Not having read up much, it would seem that one output would have to be for audio only in order to keep the hdmi/hdcp chain from seeing something not compatible.
Unfortunately I've not read of anyone that actually is using both outputs discussing the issues.
Currently, in the US market we only have one option for a UHD disk player. It is by Samsung. It has two HDMI outputs but one is for video and audio and the second is for audio only.
Your options are to connect the TV that has audio and video ( TV with speakers ) to the first hdmi that outputs both video and audio. However, if you like using an AVR for added sound and source control, you would connect your UHD player to the HDMI input to on the TV that supports 4K/ HDCP 2.2. Use the second HDMI cable from the player to your AVR. This also works for those with 4K projectors that have two HDMI inputs. The Samsung UHD player supports all optical disk formats that are current. It also has a compliment of IP TV apps for 4K content as well.
In Europe there is another player by Panasonic that uses the same connections. This Panasonic player is expected to hit US markets in August.
Currently, all UHD disk players only support HDR10. None support Dolby Vision.
There are a couple 4K AVR's now that have been firmware upgraded to support HDCP2.2 and therefore will allow your Samsung player to connect audio and video to the AVR and output HDCP 2.2 4K to your TV or Projector.
There are other compatibility issues with UHD as well. With the introduction of expanded color gamut and HDR, the player needs to be outputting the same formats as the display or the colors will all be messed up.
for example: The Samsung outputs HDR10 and 4:4:4 RGB. However my Projector wants to see 4:2:0 which means the colors are all messed up when viewing wide color gamut of BT2020. Fortunately, the colors can be recalibrated to see an acceptable picture. Not all TV's can be user recalibrated. Sony is attempting to update the firmware to fix this. The Panasonic player is supposed to output 4:2:0 wide color HDR10 so that player is claimed to be perfect out of the box when connected to the Sony projector that supports 4:2:0.
I have the Samsung player and had no problems connecting it to my projector for video to the input that supports HDCP2.2 and the audio to my AVR by the second HDMI audio only output. Just know that for 4K to work from these players, your Player and your video display must support HDCP2.2. The hdmi audio,
does not require HDCP2.2. If your TV is not HDCP compliant, then you'll need to play the 2K disk and set the player to output 1080p only.