Any cable plugged into the PI will act as an aerial for any airborne interference, RF will go everywhere and have an effect on anything.
the same piece of wire bent in a different shape can make things worse or better, it is very difficult to deal with.
standard practice is to place ferrite rings or clamps on ALL cables connected to the device having the issue, at the closest point to the effected device.
an example is this:-
these devices will reduce the interference on the cable, which is why you put then as close to the device socket as possible, but not that seen by the device its self that enters the circuit board on the PCB tracks.
Adding or removing connected parts to the PI can have positive or negative effects, it could be that the interference is nullified when the display is plugged in because the interference is getting in on that port, without a connection it is high impedance making it much more susceptible, plugging the display in will lower the connectors impedance and stop the interference, that goes the same for all sockets on any device.
All tracks on a PCB are aerials and will happily act as such unless you protect them.
This subject is a whole science in its self, I have put several product through US and EU compliance testing and am a Radio Amateur enjoying the benefits of radio.
Compliance testing is not only about the interference the device its self causes to the outside world, but also how the device its self is effected by external interference.
Give RF half a chance and it can kill a product dead unfortunately.
I personally would not deploy a PI in any commercial environment without it being in a metal enclosure, the PI is not designed, at its bare board level, to be used directly in any commercial environment without the standard precautions used on any product deployed in the same environment.
Even if you find some other cause for the issue, the comments above are the absolute minimum to consider when employing any device in an commercial environment, it is possible it will work when you test it, but if something changes when you leave and things stop working, it can be very hard to track down.
If you are going to use it with a large filed aerial then you must take some serious steps to mitigate the issues that will result from RF from that device, or any other , such as a mobile phone, wifi, POS terminal, two way radio, microwaves, bluetooth scanner, etc.
I have made a living out of rebuilding systems not designed initially with these things in mind!
I am currently working on a commercial product using the PI as its main component with serial ports and an official PI display.