I reckon the UK will negotiate a customs agreement that will be more or less the same as the existing one, but its just the name of it will change. That way everyone can save face. That would solve that movement of goods argument.
The movement of people is a whole different ball game. There will be a 500km long border between the EU (Ireland) and the UK ( N.I. ). This has nearly 600 crossing points as far as I know, not to mention walking from one side to a field to another where there is absolutely no sign of any kind of a border. There is no way to police a border so porous ( not should it be policed imo) so at the moment, any EU national is free to travel to E.G. dublin, then hop on a bus ( or even walk) to the border and just walk across. Then, because technically, you are now inside the U.K., there are no checks when travelling from Belfast to GB. The DUP in the north, wont countenance ANY passport controls up there, because that would be admitting that N.I. is somewhat "less" of a part of the UK than England, Scotland or Wales. So, now you are left with 5 options.
1. UK negotiates a deal similar to Norway - not gonna happen because that means UK abiding by EU laws
2. Create a hard border on island of Ireland - can't happen cos that will lead to violence erupting all over again , guaranteed not to mention massive job losses, particularly on the northern side
3. GB cuts NI loose - but even then it will be obliged to continue the 10 - 12 billion subvention each year for at least a decade not to mention the fact that there will probably be a civil war.
4. UK withdraws Article 50 and remains within EU. - This probably won't happen unless a deal can be done to control its own borders, which, lets be honest, is the main reason for Brexit. I would be pretty certain most people would accept this if social welfare benefits were paid at the same rate as in the country of origin. That way, you would only have people there who would contribute to the economy ( this should have been done years ago imo)
5. The nuclear option. Negotiations break down and custom posts on the border in Ireland ( bloodshed to follow) and at every port and airport. Cost of business increases. Exports become dearer so less produce sold. Imports become dearer so luxury items cost more. Now Tories will tell you that this is good for native manufacturing etc. 2 things wrong with this argument. 1. The basic resources to manufacture will have to be imported at a higher price and 2. you will only have UK nationals working in the factories. Now a lot of these voted to leave and they are not going to work for the same wages as e.g. the Latvians so the cost of produce increases, which then drives wage demands, which casues inflation, which decreases the value of sterling, which increases the cost of imports, which increases the cost of manufacturing, which increases wages, which increases inflation ...... get the picture??
There has to be a deal done. It's feckin' armageddon if there isn't.