This issue is related to chargers and cables.
Test all the chargers and cables you have and if no combination works get a charger from the community list (or the Fairphone shop) and a high quality USB data cable.
Once you found a charger/cable-combination that works make sure to treat them well. Don’t play around with the cable if you are bored and don’t rip it out of the phone or the charger, but gently unplug it.
While my previous phone also was hard to use while charging to some extent, the Fairphone 2 is absolutely unusable while connected to a power source, no matter if it’s a charger or computer.
Given the rather short lifetime (compared to a Huawei Honor, for example) I’d really prefer to be able to use it plugged in, too. Can anyone shine a light onto why this happens?