GFA isn't pre-EU, but there are pre-EU agreements in place that give UK/RoI nationals more rights than other EU Nationals have - a greater FOM and the EU felt this was unfair to other EU Nationals.
My own understanding of the GFA is that the USA played the greatest part in brokering the deal - after all the IRA did receive most of its funding via Noraid (USA based organisation). The EU were merely signatories to it.
And yes, the DUP are currently playing their hand to the fullest, but their stance is based on 'fear', and I will give them the fact that they do have a real fear of what might happen otherwise, it's more than a descriptive such as Project Fear, but something real to be fearful of.
Given the whole of the situation, I do think that there are certain exceptions that should be made by the EU in this circumstance and just saying NO, Non, Nien or Nyet is the equivalent of clutching at straws to prove a point and make things as difficult for the UK to negotiate their departure.
It would be so much easier for the EU to say ok, as far as NI is concerned, that is between the RoI and UK and we will leave you to negotiate that but we will grind your nuts on everything else.
To do otherwise is not in keeping with the EU preserving Peace throughout Europe.