HDMI I2S audio is not compatible with regular HDMI like from a Blu-Ray player. It is called "HDMI I2S" because it borrows the same physical interface (chips, cables, connectors) as the home entertainment variety. But the signals on the wires are much different and incompatible.
And RJ45 I2S and HDMI I2S format the data the same on the cable but physically are not compatible with each other. "HDMI I2S" uses LVDS balanced signals while RJ45 uses single ended TTL.