Generally you ground only one end of a shielded cable. If you ground both ends and there is a potential difference between the two locations, you can have ground currents flow between the sites via the shield. This is called an earth loop - in audio, this causes a humming or buzzing noise. For data, the electromagnetic interference from earth loops can cause data errors or reduce the overall bit rates.

If you have concerns about external interference and using STP to counter it, you really should be considering optical cabling to give total electrical and electromagnetic isolation.

Equipment cabinets are normally grounded as a normal electrical safety measure.

Your building project manager should know these sorts of things!