That's an easy one now. If we remain in the Single Market and Customs Union, then the CTA can continue unaffected.
However, unless some *middle ground* is found, if we leave the SM and CU, then all goods from and into the EU across the Irish Border will have to be policed so goods can be checked and tariffs paid, and also personal duty-free goods checked entering the EU. It will be the end of "booze cruises" so border checks would prevent cheap booze being bought in France, shipped through the Republic and into Northern Ireland.
Also the EU wouldn't approve of one of their members having free access to the UK market when the other member's don't.
So a hard border would have to be re-introduced.
A hard border splitting Ireland physically into two should meet with the full approval of Sinn Fein and the IRA*.
If we have a hard border, can someone explain what will happento the few residents in the virtual Republic exclave of the area just to the south-west of Clones where the only road access is through Northern Ireland?
https://www.openstreetmap.org/#map=12/54.1499/-7.1875
*Or maybe not. Any volunteers to ask?