I have zero experience with HDMI splitter cables.
When you connect an HDMI output device to an HDMI input device, the two systems exchange information as to the capabilities of both devices and they negotiate mutually supported connection parameters that will allow the two to function together. This exchange is called a "handshake".
I am guessing that a splitter cable connected to two display devices simultaneously will not permit two concurrent HDMI handshakes to take place, especially if the two display devices have different sets of capabilities (resolitions, supported features like Dolby, etc.)
You could connect the two displays to a single Roku through an HDMI switch that would allow you to switch back and forth between the two displays.
There are also HDMI splitter devices (as opposed to cables) where the splitter handles the handshake with the Roku and then is supposed to perform its own handhakes with the two displays. I used to try to feed the output from a Directv receiver to two different rooms via such a splitter device but never had much success.
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