At EDI there is still one door for Northern Irish arrivals and one door for Republic arrivals. They are at opposite ends of the terminal building. Up until very recently Northern Irish flights could only be boarded through 1 gate, they can now go through 2. Irish flights can presently use 3 gates. At no time will an Irish and Northern Irish flight board next to one another at EDI.
If an aircraft from NI arrives at any other stand than the one opposite the NI arrivals door then people are bussed round to it. Same for flights from the ROI. People from the ROI go through customs at EDI and collect bags from the International baggage hall, but do not go through Immigration. Not sure if customs officers are active when ROI flights arrive, but if they co-incide with another international arrival then there's not much that can be done to avoid that. The NI door leads out right next to the normal domestic arrivals area and in to the same arrivals hall and baggage reclaim as flights from London or Birmingham for example. They are just ferried past a small desk where someone stands and watches the passengers.
I agree that it's archaic in this day and age to separate people like this, but the people in charge clearly have reasons for not allowing airports to change the rules, even if it means more work and cost for airports and their staff.