A pair of matched Y capacitors on a 240V appliance from a single phase supply will cancel each other out. This doesn’t help people with 208V who are using two out of three phases, though.
edit: 120V is not immune. I once worked on a project involving powering equipment in a Faraday case at 120V. The mandatory filter (to prevent the wire from conducting emissions out of the cage) instantly tripped GFCI.
The right solution IMO would have been one of:
a) A better filter that doesn’t pass 50-60Hz. This is doable in theory, but I’ve never seen one.
b) A transformer or other isolated supply outside the cage, with a GFCI inside the cage (to protect the people who may enter to touch the equipment).
c) A transformer outside, not necessarily right next to the cage, supplying the inside with two opposite-phase lines at 60Vrms each. No net leakage! This would require that everything inside accept such a supply, which rules out anything that wants a real neutral.
d) I bet someone could design a transformer with a shield between the windings that would integrate with the Faraday cage. Power would couple in inductively through the shield. Common-mode RFI would have a very hard time escaping, and different mode RFI could be filtered and probably matters quite a bit less anyway.
Of course, the actual solution chosen by the site’s electrical people was rather less classy.