How sensitive are such devices to stray EMI? Those people would be at risk from all sorts of everyday emitters such as welders, motors with skipping brushes, vehicle ignitions, radio transmitters, etc. If this was the case, they'd need to stay home in a shielded room.

Well...an electrical engineer friend of mine, who recently had such a device implanted, told me that he's giving away his welder - because he can no longer use or be near it. No mention of dumping his microwave oven, nor cell phone, nor... Evidently the power, frequency distribution, etc. of the EMI (from the latter items) is sufficiently weak or off-frequency to ignore.

Further down, user porlune notes that one publicly-displayed Tesla coil is enclosed in what appears to be a Faraday cage. There may be liability and visitor safety reasons for that.

The article says you absolutely shouldn't build one for a science fair, and calls out the risk to disrupting pacemakers and such as a principal reason why.