Chassis ground on Ethernet RJ45 Connector
The capacitor provides a low impedance path for RF currents between the cable screen and ground.

To be effective in reducing radiation from the cable, the screen needs to be connected to the chassis earth of each device.

But as thick Ethernet provides galvanic isolation between devices, to a kV level, it wouldn't do to simply connect the two grounds together.

A 1 nF capacitor has an impedance of 1.6 ohms at 100 MHz, this is low enough to provide a good RF ground. At 60 Hz it is >2 MOhm, so it won't pass any significant current at power frequencies.

(Ethernet uses a NRZ encoding and in theory doesn't have any low frequency components, see here for some detail).

Of course this is only useful if the cable is screened. If the cable is unscreened, the capacitor will only help screening the connector chassis with its magnetics, much less important. Also, I'm surprised not to see a bleeder resistor. Anything which is isolated by a capacitor can be charged up to many kV by static in the atmosphere, in ideal conditions. When this reaches 2 or 3 kV, it breaks through and destroys the capacitor. A 1 MOhm bleeder would prevent this. Perhaps the jack already has a spark gap inside, for contact ESD.