How do the people of Donegal get along with their Northern Irish neighbors?
Reader, we marry them.
Or at least, substantial numbers of us do. Even more shift them. Nordie bucks are regarded as slightly classier than Irish men as they are less likely to wear their wellies to a club, and to show up for a date on their tractors. I confess I am less familiar with the charms of Nordie women, or how they are regarded by Donegal men: I can think of numerous marriages between Northern men and Donegal women, but none between Donegal men and Northern women come to mind. I'm sure there must be some, but I'm drawing a blank on IRL couples.
There's considerable cross-border travel for the purposes of going out. Donegal has some large nightclubs which stay open till dawn (even on Sundays!!!), Northern Ireland has comparatively cheaper booze. There's also substantial cross-border travel for shopping. Often this has been in one direction - to Northern Ireland, particularly for booze and electronics - but there's also quite a bit in the other direction, especially to the likes of Lidl and Aldi. Aldi doesn't exist in NI so that's the attraction. The other is that Lidl seems to apply the same numeric prices to their range north and south of the border, i.e., an item costing £1 in Lidl in the North costs €1 in Donegal, so it's cheaper for Northerners to shop there. Aldi is also attractive to Northerners because they have frequent price wars with Lidl, so your €1 item in Lidl could well cost 90c in Aldi.
There's a considerable degree of kinship between Donegal and Northern Ireland, because there are genuine ties of blood: most Donegal families would have Northern relatives.
Donegal is still part of Ulster (although in the Republic if Ireland) and so culturally there is not a lot of difference between those from Donegal and Those from L/Derry and Fermanagh in the neighbouring counties.
I am a wedding hair and makeup artist and travel to Donegal quite often. In honesty there's not much difference except the currency.
I assume the question came from the point of view that there is some sort of perceived war between those in Northern Ireland and those in the Republic of Ireland but that would be very inaccurate. That wasn't even the case really before the cessation of violence by paramilitaries. A lot of Northern Irish Holiday in the West coast of Donegal and so apart from the currency difference then there's no difference at all. Donegal people also have similar accents to either Fermanagh peope or L/Derry people.
Northern Ireland is actually to the east of Co. Donegal and parts of Donegal are further north than the northernmost points of Northern Ireland. Malin Head in Co. Donegal is the northernmost point in the island of Ireland.
They all get on just fine and are worried about border crossings post-Brexit.