Even among engineers with decades of experience, who have actual degrees in electrical engineering, there is controversy about this question. I've listened to both sides and have respect for them both. It isn't nearly as simple or clear-cut as some answers here have implied. There is an AES standard that covers this, but plenty of smart people shrug their shoulders at it and don't follow it.
The diverse, perverse nature of interference means that you have to stay flexible, and sometimes try a succession of different methods to solve it. A methodical approach is generally a good thing--but thus far, I've never seen one that will solve all interference problems in all situations. When you have a nasty hum or cell-phone breakthrough or a heterodyne (whistle tone) in your signal line, if you can later say "I made the problem go away" then I give you full credit for success, regardless of what you believe or don't believe about anything. If OTOH you have the right theory but you can't make the problem go away ... then not so much.
--During my misspent youth, I favored connecting pin 1 to the XLR shell on both ends of the cable, and took it for granted that that was the obvious and only way to go. But at this point, I prefer to have no direct (DC) connection on either end. Capacitive coupling as provided by Neutrik "EMC"-series XLR connectors is a relatively recent approach that can help suppress radio-frequency interference--and to what's left of my mind, that's the best solution so far, though it's no panacea.
The point is somewhat moot anyway since all microphones (that I'm aware of) hard-wire pin 1 both to signal ground and to their housings--as do most preamps, mixers and recorders, though some professional models allow ground and shield to be connected or disconnected at will.
Incidentally, that's why we're all warned never to saw off the ground lug on AC power cords, or work around a three-wire AC plug with a two-prong adapter: If an (AC-powered) preamp, mixer or recorder develops a ground fault, you presumably don't want all the microphones to suddenly carry AC line voltage on their housings; one or more performers might be the lowest-impedance path to ground.
--best regards