Still get the odd checkpoint either side of the border, with basic stop and sometimes search. These days tend to see more customs activity.. stopping for agricultural diesel.
You should be aware that its a requirement to have your driving licence with you when driving in the Republic. Also the speed limits are in KM/hr not that many people pay too much attention to it !! Beware of the rural Irish sport of "drink driving" anytime after work in the evenings.
Also its prime GAA championship (cup) season, so be wary of large cavalcades of cars with horns blazing and flags flying speeding (GAA drivers only have 2 speeds - fast and Fecking fast ) with young lads and lasses hanging out of windows as some village/parish manages to beat (7 shades out of) their neighbours in the annual grudge match. All will retire to the same pub causing an unearthly traffic jam usually at about 5PM on a Sunday. Note if there are no flags waving/youngsters hanging out of windows, it most likely a funeral which also can get rather large, cause unseeming traffic jams in rural Ireland, and also involve lots of people going to the same pub.